Grade 11 Essential Mathematics Unit 6: Measurement and Geometry


 Sabrina Allen
 2 years ago
 Views:
Transcription
1 Grade 11 Essential Mathematics Unit 6:
2 INTRODUCTION When people first began to take measurements, they would use parts of the hands and arms. For example, a digit was the width of a thumb. This kind of measurement system lacks consistency because people s bodies are all different sizes. In this unit, you will learn about measurement. Most countries around the world, including Canada, use the metric system. This system of measurement includes units such as centimetres, grams, and litres. The United States uses the Imperial system of measurement, which includes units such as miles, feet, pounds, and gallons. This unit will examine both of these systems of measurement. Assessment: o Lesson 1 Assignment: Metric and Imperial Systems o Lesson 2 Assignment: Using Formulas o Lesson 3: Assignment 1: Manipulating Area and Perimeter Formulas o Lesson 3 Assignment 2: Using Area and Perimeter Formulas o Lesson 4 Assignment: Surface Area Prisms and Cylinders o Lesson 5 Assignment: Surface Area Spheres, Pyramids, Cones o Lesson 6 Assignment: Volume o Lesson 7 Assignment: Manipulating Formulas for Surface Area and Volume o Lesson 8 Assignment: Converting Between Systems Unit Test:
3 Measurement Introduction: History of Measurement When people first began to take measurements, they would use parts of the hands and arms. For example, a digit was the width of a thumb. This kind of measurement system lacks consistency because people s bodies are all different sizes. So, using an arm length or hand span to measure a distance wasn t the best of systems. Today, there are two main systems of measurement. 1. Systeme internationale (SI) also known as the Metric System, it is used in Canada and most of the modern world. 2. Imperial System is the system that is used in the United States LESSON 1: THE METRIC SYSTEM: The metric system is an effective system because it is based on decimal numbering and all measurements are multiples of 10. This means that you can easily convert from one measurement to another just by moving the decimal. (Because moving the decimal is the same as multiplying or dividing by a multiple of 10) The primary unit (Base Unit) for measuring length is the meter. Table 1: Base Units (Metric System) Base Quantity Base Unit Symbol Length metre m Area square metre m 2 Volume cubic metre litre m 3 L Mass gram g Time second s Temperature degree Celsius C
4 Convert 150 metres to kilometres. We want to convert from Meters to Kilometers. We start at the meters and then count how many jumps are needed to get to Km. To get from meters to kilometers it is three jumps to the LEFT. This means that we move the decimal place three times to the LEFT. We have 150 m which is a whole number this means that the decimal is right at the end of the number. Convert 3500 centimetres to metres. So 150 m = km We want to convert from Centimeters to meters. We start at the centimeters and then count how many jumps are needed to get to meters. To get from meters to centimeters it is two jumps to the LEFT. This means that we move the decimal place two times to the LEFT. We have 3500 cm which is a whole number this means that the decimal is right at the end of the number. So 3500 cm = 35 m
5 Convert 14.3 km to metres. We want to convert from Kilometers to Meters. We start at the kilometers and then count how many jumps are needed to get to meters. To get from kilometers to meters it is three jumps to the RIGHT. This means that we move the decimal place three times to the RIGHT. There will be blank spaces that we fill in with zeros Convert 15.3m to mm. So 14.3 km = m We want to convert from Meters to Millimeters. We start at the meters and then count how many jumps are needed to get to millimeters. To get from meters to millimeters it is three jumps to the RIGHT. This means that we move the decimal place three times to the RIGHT. There will be blank spaces that we fill in with zeros So 15.3 km = m
6 THE IMPERIAL SYSTEM: The disadvantage of the Imperial system of measurement is that you cannot easily convert from one measurement to another as easily as we did in the Metric System. There is no common conversion factor for the imperial system; therefore, we CANNOT just move the decimal place to convert between measurements. The primary unit (base unit) for measuring length is the foot. Imperial Units Conversion Chart 1 mile = 1760 yards = 5280 feet = inches Length 1 yard = 3 feet = 36 inches 1 foot = 12 inches 1 gallon = 4 quarts Capacity 1 quart = 2 pints 1 pints = 2 cups 1 cup = 8 fluid ounces Mass 1 ton = 2000 pounds 1 pound = 16 ounces Convert 3.25 feet into inches. Convert 6 miles into yards. x inches 12 inches = 3.25 feet 1 foot 12 in x in = ( ) (3.25 ft) = 39 inches 1 ft x yards 6 miles = 1760 yards 1 mile 1760 yd x yd = ( ) (6 mi) = yd 1 mi
7 Convert 27 inches into feet. x feet 27 inches = 1 foot 12 inches x ft = ( 1 ft ) (27 in) = 2.25 ft 12 in Convert feet into miles. x miles ft = 1 mi 5280 ft x mi = ( 1 mi ) (45628 ft) = 8.6 miles 5280 ft
8 Lesson 1 Assignment: Metric and Imperial Systems Grade 11 Essentials Math See your teacher for Lesson 1 Assignment
9 Formulas: Grade 11 Essentials Math
10
11 LESSON 2: USING FORMULAS Area and Perimeter The circular target for a parachute jump has a diameter of 22.4m. To make the area more visible, the circle is filled in with chalk. One bag of chalk can cover an area of 15.5m 2. How many bags of chalk are required? 22.4m r = d 2 = = 11.2 m A = πr 2 = (3.14)( ) = (3.14)(125.44) = m 2 # of Bags = total area area one bag covers = = 25.4 bags 15.5 Shawna has a farm that is shaped like a parallelogram. The base of her land is 525m and the height is 750m. Suppose that one truck load of seed is required to plant an area of m 2, how many bags will she need to plant the entire field? 750 cm 525 cm A = bh = (525)(750) = m 2 # of trucks = # of trucks = total area area one truck covers = 31.5 truck loads
12 Find the area of the shaded portion in the diagram below. We are going to find the area of the entire rectangle first. Then we will find the area of the circle. Once we have those, we can determine the area of the shaded portion by subtracting the area of the circles from the area of the rectangles. A rectangle = ab = (10)(10) = 100 in 2 A circle = πr 2 = (3.14)(2 2 ) = (3.14)(4) = in 2 There are 4 circles so the total area for all four is: (4)(12.56) = in 2 A shaded = = in 2
13 Find the perimeter and area of the shape in the diagram below. Let us find the Perimetre first. In order to do this we need to know the length of the hypotenuse. a = 18 4 = 14 m b = = 13 m a 2 + b 2 = c = x = x = x 2 x = 365 = 19.1 m P = = m We know can find the area of each of the sections. We have to divide the original shape into sections that we have formulas for, the original shape is an irregular shape for which we don t have a formula. A 1 = LW = (18)(26) = 468 m 2 A 2 = bh 2 = (13)(14) 2 A total = = 611 m 2 = 91 m 2 A 3 = LW = (4)(13) = 52 m 2
14 Curriculum Outcomes: 11E3.G Develop an understanding of spatial relationships Lesson 2 Assignment: Using Formulas See your teacher for Lesson 2 Assignment
15 LESSON 3: MANIPULATING AREA AND PERIMETER FORMULAS We will be using the formulas for area and perimeter to solve for one of the missing lengths given an area or perimeter. If the area of a rectangular backyard is 90m 2 and it has a length of 11.25m what is the width of the yard? a = b =? A = 90 m 2 90 = (11.25)(b) 90 = (11.25)(b) m = b If the area of a triangle is 125cm 2 and the base is 15cm long how tall is this triangle? A = 125 cm 2 h =? 15 cm A = bh = (15)(h) = (7.5)(h) h = = 16.7 cm
16 The perimeter of a rectangle is 68.8 feet and it has a length of 17.5 feet, what is the width? b =? P = 68.8 ft P = 2a + 2b a = 17.5 ft 68.8 = (2)(17.5) + (2)(b) 68.8 = 35 + (2)(b) = (2)(b) 33.8 = (2)(b) = b b = 16.9 ft A circle has an area of cm 2 what is the radius? r =? A = cm 2 A = r = (3.14)(r 2 ) = r2 36 = r 2 36 = r r = 6 cm
17 A circle has a circumference of mm, what is the diameter? r =? C = cm C = 2 r = (2)(3.14)(r) = (6.28)(r) = r r = 5.5 mm d = 2r = (2)(5.5) = 11 mm You are painting one all in your room. It measures 12 feet long and has an area of 84 ft 2. What is the height of the wall? If one can of paint covers 25 ft 2, how many cans will you need to paint your wall? H =? A = LW 84 = (12)(H) L = 12ft = H H = 7 ft # of cans of paint = total area to paint area one can will paint = 84 = 3.36 cans of paint 25
18 A rectangular shaped window has a semicircle stained glass decorative piece attached to the top. If the area of the entire window is 215.2m 2 and the stained glass portion has a diameter of 5m what are the dimensions of the rectangular window? A total = m 2 d = 5m r = d 2 = 5 2 = 2.5m A half circle = r2 2 = (3.14)(2.52 ) = (3.14)(6.25) = = 9.8 m A rectangle = = 205.4m 2 A = LW = (5)(W) = (5)(W) m = W
19 Curriculum Outcomes: 11E3.G Develop an understanding of spatial relationships Lesson 3: Assignment: Manipulating Area and Perimeter Formulas See your teacher for Lesson 3 Assignment
20 Curriculum Outcomes: 11E3.G Develop an understanding of spatial relationships Lesson 3 Assignment 2: Using Area and Perimeter Formulas See your teacher for Lesson 3 Assignment 1
21 LESSON 4: FINDING SURFACE AREA Prisms and Cylinders Find how much paint is required to cover a wooden cabinet that has dimensions of 24 inches wide, 48 inches tall and 16 inches deep. You will need two coats of paint and one can of paint will cover 8 ft 2. SA = 2LW + 2LH + 2WH 48 in = = 4 ft SA = (2)(2)(1.33) + (2)(2)(4) + (2)(1.33)(4) SA = SA = ft 2 24 in = = 2 ft 16 in = 16 = 1.33 ft 12 Need two Coats of Paint: SA Total = (2)(31.96) = ft 2 # of cans = total area to paint area one covers # of cans = 64 8 = 8 cans of paint
22 A water tower is cylindrical in shape with a height of 8.6m and a diameter if 33m. How much surface area would be painted if the top and sides of three water towers need to be repainted? d = 33m diameter = 33m radius = r = d 2 = 33 2 = 16.5 m H = 8.6m Reading the question it says that the top and the sides are painted which means that the bottom of the tower is not painted. So we need to make sure that we change the formula accordingly. SA = 2πrh + 2πr 2 SA = 2πrh + πr 2 SA = (2)(3.14)(16.5)(8.6) + (3.14)( ) SA = = = 1746 m 2 There are three towers to be painted: SA = (3)(1746) = 5238 m 2
23 The wood that Terrance wants to use to make a shelving unit costs $6.49/ft 2. How much will it cost him (assuming no wastage) to make a shelving unit that is 4 ft wide by 12 inches deep by 5 ft tall if there are 4 shelves (plus the top and bottom)? We don t have a formula that is in this shape so we need to look at the shapes individually. There are two sides on this bookcase. Back of the bookcase: 5 ft 5 ft 12 = 12inches = 1 foot 4 ft A = LW = (4)(5) = 20 ft 2 A sides = 2LW = (2)(5)(1) = 10 ft 2 Shelves and the top and bottom: Six in total 1 ft 4 ft A = 6(L)(W) = (6)(4)(1) = 24 ft 2 Total Surface Area = = 54 ft 2 Cost = ($6.49)(54) = $350.46
24 You are looking for a new tent (triangle prism) to go camping this summer. You have found one that has a height of 5 feet and 6 inches, is 5 feet wide and 7 feet long. You want to know how much material was used to make this tent. Again we don t have a formula for this shape. We need to split this into shapes for which we have formulas. 5.5 ft 5 ft 7 ft Front and Back: 5.5 ft SA front/back = 2 ( bh 2 ) = 2 ((5)(5.5)) = 2(13.75) = 27.5 ft ft Botttom: SA = LW = (5)(7) = 35 ft 2 7 ft 5 ft
25 Sides: We don t know that length of the slanted side of the tent. We will need to find this before we can find the area of the sides. s 7 ft In order to find the length of the slanted side we need to use Pythagorean Theorem. To do this, we need to have a right angle triangle = s ft s = s = s 2 5 ft 2.5 ft s = 36.5 = 6.04 ft Now that we have the length of the slanted side we can use it to determine the area of the sides of the tent. A sides = 2LW = (2)(7)(6.04) = 84.6 ft 2 SA total = = ft 2
26 Curriculum Outcomes: 11.E3.G.1 Solve problems that involve SI and imperial units in surface area measurements Grade 11 Essentials Math Lesson 4 Assignment: Surface Area Prisms and Cylinders See your teacher for Lesson 4 Assignment
27 LESSON 5: FINDING SURFACE AREA Pyramids, Spheres, and Cones Determine the surface area of a cone if it has a radius of 3.4m and a slant height of 12.2m. 3.4m SA = πr 2 SA = (3.14)(3.4 2 ) 12.3m SA = (3.14)(11.56) SA = 36.3 m 2 What is the surface area of a sphere with diameter of 2.5 feet? The formula for SA requires the radius, given the diamter so we need to divide by 2 to find the radius. r = d 2 = = 1.25ft SA = 4πr 2 SA = (4)(3.14)( ) SA = (4)(3.14)(1.5625) SA = 19.6 ft 2
28 A child s tent is the shape of a triangular prism. If it has a slant height of 4 feet, a width of 6 feet and a length of 6 feet, what is the surface area of the canvas required to build the tent? What would the surface area of the tent be if it were a square based pyramid in shape? We don t have a formula for this shape so we will need to find the area of each of the pieces that make up this tent. SA sides = LW = (6)(4) = 24ft 2 4ft There are two sides so: SA sides = (2)(24) = 48 ft 2 SA bottom = LW = (6)(6) = 36ft 2 6ft 6ft We now need to find the SA of the triangular sides To do this we need to know the height of the tent. We will use Pythagorean Theroem to determine the height. We will need a Right Angle Triangle to use Pythagorean Theroem a 2 + b 2 = c b 2 = b 2 = 16 b 2 = 16 9 b a = 3 ft 6 ft c = 4 ft b = 7 = 2.6 SA front back = bh 2 = (6)(2.6) 2 = 7.8 ft 2 There are two triangles so: SA front back = (2)(7.8) = 15.6 ft 2 SA total = = 99.6 ft 2
29 We have a formula for the Surface Area of this shape so we just need to use it. SA = 2sb + b 2 4ft SA = (2)(4)(6) SA = = 84 ft 2 6ft 6ft
30 Curriculum Outcomes: 11.E3.G.1 Solve problems that involve SI and imperial units in surface area measurements Grade 11 Essentials Math Lesson 5 Assignment: Surface Area Spheres, Pyramids, Cones See your teacher for Lesson 5 Assignment
31 LESSON 6: VOLUME Find the volume for the following shapes: V = LWH = (2)(2)(12) = 48cm 3 V = BHL 2 = (20)(15)(30) = 9000 = 4500 mm 2 2 2
32 We need the radius for the Volume formula. r = d 2 = 6 2 = 3 in V = πr 2 h V = (3.14)(3 2 )(4) V = (3.14)(9)(4) V = in 2 Calculate the volume of the space left after a square based pyramid has been removed from the rectangular solid. Assume that the pyramid and the rectangle are the same height. To find the amount of space left we need to know the volume of each shape. V rectangle = LWH = (6)(6)(8.5) = 306 cm 3 V pyramid = b2 h 3 = (62 )(8.5) = (36)(8.5) = 306 = 102 cm V space = = 204 cm 3
33 Paul wants to cover an area of yard that is 10.8m by 9.5 m with 10cm of topsoil. How much topsoil does he need to order? How much will it cost if the soil is $18.75/m 3? H 10cm 10.8m L 9.5m W We need to make sure that all the units are the same. Since the questions is asking for the cost and it is in m 3 it is easiest to have all the units in meters. We need to have the Height in meters, H = 10 cm = 0.10 m V = LWH = (10.8)(9.5)(0.10) = m 3 A grain hopper is in the shape of an inverted cone on the bottom of a cylinder. The hopper has a diameter of 48 inches, a height of 8 feet. The cylinder has a height of 45 inches. How much will the hopper hold once built? 48in First we need to have all the units in the same measure. Let us choose Feet but Inches would also be correct. 45 in H cylinder = 45 inches = = 3.75ft diameter = 48 in = = 4ft 8ft radius = 4 2 = 2ft H cone = = 4.25ft V cylinder = πr 2 h = (3.14)(2 2 )(3.75) = 47.1 ft 3 We need to know the height of the cone. H cone = = 4.25 ft V cone = πr2 h 3 = (3.14)(22 )(4.25) = (3.14)(4)(4.25) = = 17.8ft V total = = 64.9 ft 3
34 Tennis balls are usually sold in cylindrical containers that often hold 3 tennis balls. If each tennis ball has a radius of 3.4cm, what are the dimensions of the cylindrical container that holds three tennis balls? What is the volume of one tennis ball? What is the volume of the container? r r = 3.4 cm The radius of the tennis ball is also the radius of the cylinder Three tennis balls stacked will give us the height of the cylinder Each tennis ball has a diameter of 6.8 cm so three stacked is H cylinder H cylinder = (3)(d) = (3)(6.8) = 20.4 cm Dimensions of the Cylinder: r = 3.4cm H = 20.4 cm V tennis ball = (4)(3.14)(39.3) 3 V tennis ball = 4πr3 3 = (4)(3.14)(3.43 ) 3 = = 164.6cm 3 V cylinder = πr 2 h = (3.14)(3.4 2 )(20.4) = (3.14)(11.56)(20.4) = cm 3
35 Curriculum Outcomes: 11.E3.G.2 Solve problems that involve SI and imperial units in volume and capacity measurements Lesson 6 Assignment: Volume Grade 11 Essentials Math See your teacher for Lesson 6 Assignment
36 LESSON 7: MANIPULATION OF SURFACE AREA AND VOLUME FORMULAS: We won t always be calculating the surface area or volume of objects. Sometimes we are given this information and we need to solve for a side length or a height or the radius of the object. When we are given the Surface Area or the Volume and asked to find the missing side this requires us to manipulate the formula to solve for what we have been asked to determine. The surface area of paper required to cover a soup can is cm 2. If the radius of the soup can is 4 cm, how tall is it? r = 4cm SA = cm 2 The label on a soup can only goes around the can so we don t need to include the top and the bottom in the formula for Surface Area. /// SA = 2πr 2 + 2πrh = 2πrh Now that we have the correct formula we will substitute the values in where they belong in the formula and solve for the height SA = 2πrh = (2)(3.14)(4)(h) = (25.12)(h) = (25.12)(h) cm = h
37 What is the radius of a soup can if the height is 7 cm and its volume is cm 3? Grade 11 Essentials Math V = cm 3 h = 7in Here we are given the Volume of the can. V = πr 2 h Now substitute in the values that are given in the question = (3.14)(r 2 )(7) We want to solve for the radius so we will simplify the right hand side as much as possible = (21.98)(r 2 ) = (21.98)(r2 ) = r 2 9 = r r = 3cm
38 What is the radius of a cone if its height is 14 inches and the volume is in 3? Grade 11 Essentials Math h = 14in V = in 3 We are given the Volume of a cone: V = πr2 h Substitute in the equation the values given in the question = (3.14)(r2 )(14) 3 Simplify the Right Hand side as much as possible first = (43.96)(r2 ) = (14.65)(r 2 ) = (14.65)(r2 ) = r 2 9 = r r = 3 in What is the radius of a spherical balloon if it has a volume of in 3? We have the volume of a sphere: V = 4πr = (4)(3.14)(r3 ) = (12.56)(r3 ) = (4.19)(r 3 ) = (4.19)(r3 ) = r = r r = 5.5cm
39 What is the slant height of a square based pyramid if the surface area 4095m 2 is and the length of its base is 23m? SA = 4095m 2 SA = 2sb + b 2 s 4095 = (2)(s)(23) + (23 2 ) 23m 23m Simplify the right side as much as possible 4095 = (46)(s) We need to subtract the before we can solve for s = (46)(s) = (46)(s) = (46)(s) m = s
40 Curriculum Outcomes: 11.E3.G.3 Solve problems that require the manipulation and application of formulas related to surface area and volume Lesson 7 Assignment: Manipulating Formulas for Surface Area and Volume See your teacher for Lesson 7 Assignment
41 LESSON 8: CONVERTING BETWEEN SYSTEMS Length Conversion Metric (SI) unit Imperial unit 1 millimetre (mm) inches (in) 1 centimetre (cm) 0.39 inches (in) feet (ft) 1 metre (m) inches (in) 3.28 feet (ft) 1.09 yards (yd) 1 kilometre (km) 0.62 miles Examples (round to 1 decimal): a. Convert 2 cm to inches x inches 2 cm = 0.39 inches 1 cm x cm = (2 cm)(0.39 in) 1 cm = 0.78 cm b. Convert 1.7 m to yards x yards = c. Convert 4.5 miles to kilometres x yards 1.7 m = 1.09 yards 1 m (2 cm)(0.39 in) 1 cm x km 4.5 miles = 1 km 0.62 miles = yds x km = (1 km)(4.5 miles) 0.62 miles = 7.26 km d. Convert 6.3 feet to metres x m 6.3 feet = 1 m 3.28 ft x cm = (1 m)(6.3 ft) 3.28 ft = 1.92 m
42 Rebecca is planning to install sod in her backyard, which is 18.2 m by 9.8 m. If sod costs $0.28/ft 2, how much will it cost to sod the backyard? 18.2m 9.8m The first step is to make sure that we have matching units. The cost is given in Feet but the measurements for the yard are in Meters. We need to change the Meters to Feet. Length: x feet 3.28 ft = 18.2 m 1 m x ft = (18.2 m)(3.28 ft) 1 m = ft Width: x feet 9.8 m = 3.28 ft 1 m x ft = (9.8 m)(3.28 ft) 1 m = ft Now we can find the area of the yard: A = LW = (59.07)(32.14) = ft 2 Cost = ($0.28)( ) = $537.25
43 You would like to replace the carpet in your living room and have measured it to be 12ft by 15ft. The price of the carpet that you want is $24.99/m 2. How much carpet do you need to buy? What will this cost you (before taxes)? 12 ft 15 ft The first step is to make sure that we have matching units. The cost is given in Meters but the measurements for the yard are in Feet. We need to change the Feet to Meters. x m = (12 ft)(1 m) 3.28 ft Length: = 3.66 m x m 12 ft = 1 m 3.28 ft Width: x m 15 ft = 1 m 3.28 ft x m = (15 ft)(1 m) 3.28 ft = 4.57 m Now we can find the area of the yard: A = LW = (3.66)(4.57) = m 2 Cost = ($24.99)(16.73) = $ A landscaper needs to estimate the amount of material required for a project building a circular brick patio for a client. The diameter of the patio is 13m and one bundle of brick will cover 116ft 2. How many bundles does he need? 13m Need the units in Feet: x ft 13 m = 3.28 ft 1 m (13m)(3.28 ft) x ft = = ft 1 m We will need the Radius: r = d 2 = = ft 2 A = πr 2 = (3.14)( ) = (3.14)(454.54) = ft 2 Number of Bundles = Total area to cover area one bundle covers = = 12.3 bundles 116
44 Curriculum Outcomes: 11.E3.G.3 Solve problems that require the manipulation and application of formulas related to surface area and volume Lesson 8 Assignment: Converting Between Systems See your teacher for Lesson 8 Assignment
FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication
FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby
More informationUnit 1 Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
Unit 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Convert 8 yd. to inches. a. 24 in. b. 288 in. c. 44 in. d. 96 in. 2. Convert 114 in. to yards,
More informationPerimeter, Area, and Volume
Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all
More informationArea of Parallelograms, Triangles, and Trapezoids (pages 314 318)
Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base
More informationSolids. Objective A: Volume of a Solids
Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular
More informationTeacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 91.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
More informationIn Problems #1  #4, find the surface area and volume of each prism.
Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1  #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR
More informationCalculating the surface area of a threedimensional object is similar to finding the area of a two dimensional object.
Calculating the surface area of a threedimensional object is similar to finding the area of a two dimensional object. Surface area is the sum of areas of all the faces or sides of a threedimensional
More informationArea is a measure of how much space is occupied by a figure. 1cm 1cm
Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number
More informationCharacteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
More informationGrade 6 FCAT 2.0 Mathematics Sample Questions
Grade FCAT. Mathematics Sample Questions The intent of these sample test materials is to orient teachers and students to the types of questions on FCAT. tests. By using these materials, students will become
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationPerimeter, Area, and Volume
Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the
More information1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft
2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite
More informationMAT104: Fundamentals of Mathematics II Summary of Section 145: Volume, Temperature, and Dimensional Analysis with Area & Volume.
MAT104: Fundamentals of Mathematics II Summary of Section 145: Volume, Temperature, and Dimensional Analysis with Area & Volume For prisms, pyramids, cylinders, and cones: Volume is the area of one base
More information124 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h
Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h The volume is 108 cm 3. The volume V of a prism is V = Bh, where B is the area of a base and h the
More informationGeometry Notes VOLUME AND SURFACE AREA
Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate
More informationChapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green WorkedOut Solutions. Try It Yourself (p. 353) Number of cubes: 7
Chapter 8 Opener Try It Yourself (p. 5). The figure is a square.. The figure is a rectangle.. The figure is a trapezoid. g. Number cubes: 7. a. Sample answer: 4. There are 5 6 0 unit cubes in each layer.
More informationArea of Parallelograms (pages 546 549)
A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular
More informationHeight. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.
Name: Period GL UNIT 11: SOLIDS I can define, identify and illustrate the following terms: Face Isometric View Net Edge Polyhedron Volume Vertex Cylinder Hemisphere Cone Cross section Height Pyramid Prism
More informationCONNECT: Volume, Surface Area
CONNECT: Volume, Surface Area 1. VOLUMES OF SOLIDS A solid is a threedimensional (3D) object, that is, it has length, width and height. One of these dimensions is sometimes called thickness or depth.
More informationCalculating Area, Perimeter and Volume
Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly
More informationIntegrated Algebra: Geometry
Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and
More informationMEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.
MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units
More informationGeometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
More informationGrade 8 FCAT 2.0 Mathematics Sample Questions
Grade FCAT. Mathematics Sample Questions The intent of these sample test materials is to orient teachers and students to the types of questions on FCAT. tests. By using these materials, students will become
More informationACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.
8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates
More informationVOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.
Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:
More informationPizza! Pizza! Assessment
Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the
More informationGAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book
GAP CLOSING Volume and Surface Area Intermediate / Senior Student Book Volume and Surface Area Diagnostic...3 Volumes of Prisms...6 Volumes of Cylinders...13 Surface Areas of Prisms and Cylinders...18
More informationShow that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.
Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional
More informationObjective To introduce a formula to calculate the area. Family Letters. Assessment Management
Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment
More informationLesson 18 Pythagorean Triples & Special Right Triangles
Student Name: Date: Contact Person Name: Phone Number: Teas Assessment of Knowledge and Skills Eit Level Math Review Lesson 18 Pythagorean Triples & Special Right Triangles TAKS Objective 6 Demonstrate
More informationSURFACE AREA AND VOLUME
SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More information12 Surface Area and Volume
12 Surface Area and Volume 12.1 ThreeDimensional Figures 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders 12.5 Volumes of Pyramids
More informationPractice: Space Figures and Cross Sections Geometry 111
Practice: Space Figures and Cross Sections Geometry 111 Name: Date: Period: Polyhedron * 3D figure whose surfaces are * each polygon is a. * an is a segment where two faces intersect. * a is a point where
More informationGrade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference
1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various
More informationImperial Length Measurements
Unit I Measuring Length 1 Section 2.1 Imperial Length Measurements Goals Reading Fractions Reading Halves on a Measuring Tape Reading Quarters on a Measuring Tape Reading Eights on a Measuring Tape Reading
More informationVolume of Spheres. A geometric plane passing through the center of a sphere divides it into. into the Northern Hemisphere and the Southern Hemisphere.
Page 1 of 7 9.6 Surface Area and Volume of Spheres Goal Find surface areas and volumes of spheres. Key Words sphere hemisphere A globe is an example of a sphere. A sphere is the set of all points in space
More informationVirginia Mathematics Checkpoint Assessment MATHEMATICS 5.8. Strand: Measurement
Virginia Mathematics Checkpoint Assessment MATHEMATICS 5.8 Strand: Measurement Standards of Learning Blueprint Summary Reporting Category Grade 5 SOL Number of Items Number & Number Sense 5.1, 5.2(ab),
More informationLESSON SUMMARY. Measuring Shapes
LESSON SUMMARY CXC CSEC MATHEMATICS UNIT SIX: Measurement Lesson 11 Measuring Shapes Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1 (Some helpful exercises and page numbers are given
More informationRevision Notes Adult Numeracy Level 2
Revision Notes Adult Numeracy Level 2 Place Value The use of place value from earlier levels applies but is extended to all sizes of numbers. The values of columns are: Millions Hundred thousands Ten thousands
More information103 Area of Parallelograms
03 Area of Parallelograms MAIN IDEA Find the areas of parallelograms. NYS Core Curriculum 6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest,
More informationYOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!
DETAILED SOLUTIONS AND CONCEPTS  SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Santa Monica College COMPASS Geometry Sample Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the area of the shaded region. 1) 5 yd 6 yd
More informationTallahassee Community College PERIMETER
Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides
More informationB = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3
45 Volume Surface area measures the area of the twodimensional boundary of a threedimensional figure; it is the area of the outside surface of a solid. Volume, on the other hand, is a measure of the space
More informationGrade 7/8 Math Circles Winter D Geometry
1 University of Waterloo Faculty of Mathematics Grade 7/8 Math Circles Winter 2013 3D Geometry Introductory Problem Mary s mom bought a box of 60 cookies for Mary to bring to school. Mary decides to bring
More informationArea LongTerm Memory Review Review 1
Review 1 1. To find the perimeter of any shape you all sides of the shape.. To find the area of a square, you the length and width. 4. What best identifies the following shape. Find the area and perimeter
More informationof surface, 569571, 576577, 578581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationArea of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in
More informationThird Grade Illustrated Math Dictionary Updated 91310 As presented by the Math Committee of the Northwest Montana Educational Cooperative
Acute An angle less than 90 degrees An acute angle is between 1 and 89 degrees Analog Clock Clock with a face and hands This clock shows ten after ten Angle A figure formed by two line segments that end
More informationBasic Math for the Small Public Water Systems Operator
Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the
More informationLesson 17 ~ Volume of Prisms
Lesson 17 ~ Volume of Prisms 1. An octagonal swimming pool has a base area of 42 square meters. The pool is 3 feet deep. Find the volume of the pool. 2. A fish aquarium is a rectangular prism. It is 18
More informationMATH 110 Landscape Horticulture Worksheet #4
MATH 110 Landscape Horticulture Worksheet #4 Ratios The math name for a fraction is ratio. It is just a comparison of one quantity with another quantity that is similar. As a Landscape Horticulturist,
More informationFundamentals of Geometry
10A Page 1 10 A Fundamentals of Geometry 1. The perimeter of an object in a plane is the length of its boundary. A circle s perimeter is called its circumference. 2. The area of an object is the amount
More informationWEIGHTS AND MEASURES. Linear Measure. 1 Foot12 inches. 1 Yard 3 feet  36 inches. 1 Rod 5 1/2 yards  16 1/2 feet
WEIGHTS AND MEASURES Linear Measure 1 Foot12 inches 1 Yard 3 feet  36 inches 1 Rod 5 1/2 yards  16 1/2 feet 1 Furlong 40 rods  220 yards  660 feet 1 Mile 8 furlongs  320 rods  1,760 yards 5,280 feet
More informationInstallation Patterns Using Cambridge Pavingstones With ArmorTec. The ArmorTec Advantage. Cambridge Pavers, Inc. PO Box 157 Lyndhurst, NJ
DesignScaping Installation Patterns Using Cambridge Pavingstones With ArmorTec Imagine... with dozens of Cambridge shapes and colors to choose from, you can create your own personal design for a driveway,
More informationGeometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
More informationArea and Circumference
4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert
More informationCONNECT: Volume, Surface Area
CONNECT: Volume, Surface Area 2. SURFACE AREAS OF SOLIDS If you need to know more about plane shapes, areas, perimeters, solids or volumes of solids, please refer to CONNECT: Areas, Perimeters 1. AREAS
More informationName: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:
Name: Date: Geometry Honors 20132014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 16 HW: Pgs: 710 DAY 2: SWBAT: Calculate the Volume
More informationSolving Equations With Fractional Coefficients
Solving Equations With Fractional Coefficients Some equations include a variable with a fractional coefficient. Solve this kind of equation by multiplying both sides of the equation by the reciprocal of
More informationPerfume Packaging. Ch 5 1. Chapter 5: Solids and Nets. Chapter 5: Solids and Nets 279. The Charles A. Dana Center. Geometry Assessments Through
Perfume Packaging Gina would like to package her newest fragrance, Persuasive, in an eyecatching yet costefficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters
More informationMATHEMATICS  SCHEMES OF WORK
MATHEMATICS  SCHEMES OF WORK For Children Aged 7 to 12 Mathematics Lessons Structure Time Approx. 90 minutes 1. Remind class of last topic area explored and relate to current topic. 2. Discuss and explore
More informationFinding Volume of Rectangular Prisms
MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of threedimensional composite shapes.
More informationGEOMETRY (Common Core)
GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Wednesday, August 12, 2015 8:30 to 11:30 a.m., only Student Name: School Name: The
More informationQuick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More informationConverting Units of Measure Measurement
Converting Units of Measure Measurement Outcome (lesson objective) Given a unit of measurement, students will be able to convert it to other units of measurement and will be able to use it to solve contextual
More informationThe Area is the width times the height: Area = w h
Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what
More informationThe GED math test gives you a page of math formulas that
Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding
More informationArea of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of
More information43 Perimeter and Area
43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study
More informationCHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS
CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change
More informationMath Tech 1 Unit 11. Perimeter, Circumference and Area. Name Pd
Math Tech 1 Unit 11 Perimeter, Circumference and Area Name Pd 111 Perimeter Perimeter  Units  Ex. 1: Find the perimeter of a rectangle with length 7 m and width 5 m. Ex. 2: Find the perimeter of the
More informationSurface Area of Prisms
Surface Area of Prisms Find the Surface Area for each prism. Show all of your work. Surface Area: The sum of the areas of all the surface (faces) if the threedimensional figure. Rectangular Prism: A prism
More informationExercise Worksheets. Copyright. 2002 Susan D. Phillips
Exercise Worksheets Copyright 00 Susan D. Phillips Contents WHOLE NUMBERS. Adding. Subtracting. Multiplying. Dividing. Order of Operations FRACTIONS. Mixed Numbers. Prime Factorization. Least Common Multiple.
More information17.2 Surface Area of Prisms and Cylinders
Name Class Date 17. Surface Area of Prisms and Cylinders Essential Question: How can you find the surface area of a prism or cylinder? Explore G.11.C Apply the formulas for the total and lateral surface
More informationDIMENSIONAL ANALYSIS #2
DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we
More informationRight Prisms Let s find the surface area of the right prism given in Figure 44.1. Figure 44.1
44 Surface Area The surface area of a space figure is the total area of all the faces of the figure. In this section, we discuss the surface areas of some of the space figures introduced in Section 41.
More informationAssessment For The California Mathematics Standards Grade 3
Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,
More informationALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only
ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The
More informationDIMENSIONAL ANALYSIS #2
DIMENSIONAL ANALYSIS #2 Area is measured in square units, such as square feet or square centimeters. These units can be abbreviated as ft 2 (square feet) and cm 2 (square centimeters). For example, we
More informationSA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid
Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.
More informationMEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were:
MEASUREMENT Introduction: People created systems of measurement to address practical problems such as finding the distance between two places, finding the length, width or height of a building, finding
More informationVolume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms.
Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts
More informationFormulas for Area Area of Trapezoid
Area of Triangle Formulas for Area Area of Trapezoid Area of Parallelograms Use the formula sheet and what you know about area to solve the following problems. Find the area. 5 feet 6 feet 4 feet 8.5 feet
More informationMeasurement/Volume and Surface Area LongTerm Memory Review Grade 7, Standard 3.0 Review 1
Review 1 1. Explain how to convert from a larger unit of measurement to a smaller unit of measurement. Include what operation(s) would be used to make the conversion. 2. What basic metric unit would be
More information2nd Semester Geometry Final Exam Review
Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular
More informationEach pair of opposite sides of a parallelogram is congruent to each other.
Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite
More informationSolving Geometric Applications
1.8 Solving Geometric Applications 1.8 OBJECTIVES 1. Find a perimeter 2. Solve applications that involve perimeter 3. Find the area of a rectangular figure 4. Apply area formulas 5. Apply volume formulas
More informationArea and Volume Equations
Area and Volume Equations MODULE 16? ESSENTIAL QUESTION How can you use area and volume equations to solve realworld problems? LESSON 16.1 Area of Quadrilaterals 6.8.B, 6.8.D LESSON 16. Area of Triangles
More informationCARPENTRY MATH ASSESSMENT REVIEW
CARPENTRY MATH ASSESSMENT REVIEW This material is intended as a review. The following Learning Centres have more resources available to help you prepare for your assessment Nanaimo ABE Learning Centre:
More informationImperial and metric quiz
Level A 1. Inches are a metric measure of length. 2. Pints are smaller than gallons. 3. 1 foot is the same as: A) 12 inches B) 14 inches C) 16 inches D) 3 yards 4. foot is usually shortened to: A) 1 f
More informationSurface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry
Surface Area of Rectangular & Right Prisms Surface Area of Pyramids Geometry Finding the surface area of a prism A prism is a rectangular solid with two congruent faces, called bases, that lie in parallel
More informationCIRCUMFERENCE AND AREA OF CIRCLES
CIRCUMFERENCE AND AREA F CIRCLES 8..1 8.. Students have found the area and perimeter of several polygons. Next they consider what happens to the area as more and more sides are added to a polygon. By exploring
More informationUNIT 1 MASS AND LENGTH
UNIT 1 MASS AND LENGTH Typical Units Typical units for measuring length and mass are listed below. Length Typical units for length in the Imperial system and SI are: Imperial SI inches ( ) centimetres
More informationChapter 19. Mensuration of Sphere
8 Chapter 19 19.1 Sphere: A sphere is a solid bounded by a closed surface every point of which is equidistant from a fixed point called the centre. Most familiar examples of a sphere are baseball, tennis
More informationFSA Geometry EndofCourse Review Packet. Modeling and Geometry
FSA Geometry EndofCourse Review Packet Modeling and Geometry MAFS.912.GMG.1.1 EOC Practice Level 2 Level 3 Level 4 Level 5 uses measures and properties to model and describe a realworld object that
More information