Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Calculating the surface area of a three-dimensional object is similar to finding the area of a two dimensional object."

Transcription

1

2 Calculating the surface area of a three-dimensional 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 three-dimensional object. Therefore, to calculate surface area of an object you must find the area of all sides and then add them together.

3 l w h A lw A (5)(3) l A 15cm w SA lw lh wh SA (5)(3) (5)(4) (3)(4) SA 94cm

4 Did You Know? A net is a two dimensional representation of a three dimensional object? Nets can be very helpful when calculating the surface area of a threedimensional object. Here is the net for the previous rectangular prism:

5 The circumference is an important measurement when determining the surface area of a cylinder as you will see in the next example. The circumference (perimeter) of a circle is C = πd where d is the diameter of the circle, or C = πr where r is the radius of the circle. Therefore, surface area of a cylinder can be calculated using the formula SA r dh Where d is the diameter of the cylinder SA r rh Where r is the radius of the cylinder

6 Find the surface area for the cylinder below: 10 cm 9 cm SA r rh SA (5) SA 439.8cm (5)(9) For radius = diameter / = 10 / = 5

7 Find the surface area for the triangular prism below: Step 1 Find the area of the triangular ends (there are of them!) h 5 cm 7 cm b 0 cm bh A [7][5] A A 17.5 A 35cm

8 Find the surface area for the triangular prism below: 5 cm 7 cm w 0 cm l Step Determine the area of the rectangular bottom A lw A (0)(7) A 140cm

9 Find the surface area for the triangular prism below: Step 3 Determine the area of the rectangular sides (there are two of them!) 6.1 cm 5 cm 7 cm 5 cm b c 3.5 cm a 6.1 cm 0 cm We only know the length (0 cm) We must solve for the width using Pythagorean Theorem c c c a b ( 3.5) (5) c 37.5 c 37.5 c 6. 1cm Therefore, for the Area: A ( lw) A (0)(6.1) A 1 A 44cm

10 Find the surface area for the triangular prism below: Step 4 Add up all the Areas 6.1 cm 5 cm 7 cm 0 cm Total Surface Area = A TRIANGLE SIDES + A RECTANGULAR BOTTOM + A RECTANGULAR SIDE = = 419 cm Therefore, total surface area of the prism is 419 square centimetres. Now that you have had the opportunity to calculate the surface area of prisms, you will apply this knowledge to solve some real-world applications. END OF DAY 1

11 Joel s bedroom is 1 feet by 15 feet and the height from the floor to the ceiling is 10ft. He decides he is going to paint his bedroom walls dark green and the ceiling white. To ensure full coverage, the entire room will require two coats of paint. If a 1 gallon can of paint covers approximately 400 square feet, how many cans of each colour of paint, green and white, does Joel need to purchase? SOLUTION 10 feet We need to find the area of each given side (the 4 walls and the roof) and then find out the amount of paint for each colour 15 feet 1 feet

12 10 feet 15 feet 1 feet Step 1 Find area of front walls (there are two of them!) Step Find area of side walls (there are two of them!) Area = (lw) = [(1)(10)] = (10) = 40 ft Area = (lw) = [(15)(10)] = (150) = 300 ft Total wall area = = 540 ft

13 Step 3 Find the number of cans of paint to cover the walls 10 feet 15 feet Given that the total wall area is 540 ft and that two coats of paint are needed... Total area to be covered is 540 = 1080 ft. 1 feet # of cans = total area / area covered by one gallon can = 1080 ft / 400 ft =.7 gallon cans Therefore 3 gallon cans of green paint should be used to cover the walls

14 Step 4 Find the area of the roof 1 feet 10 feet 15 feet A = lw = (15)(1) = 180 ft Step 5 Determine the # of gallon cans required Since two coats are required 180 = 360 ft # of cans = total area / area covered by one gallon can = 360 ft / 400 ft = 0.9 gallon cans Therefore, only one can of white paint is required to paint the roof

15 Christmas time is approaching and you have purchased the same gift for each of your 14 co-workers. The gifts are packaged in boxes with dimensions by 1 5 by If there are 80 square feet of wrapping paper per roll, how many rolls of wrapping paper do you require to wrap all your gifts? / 1 = 0.17 ft. Total = =.17 ft / 1 = 0.9 ft. Total = = 1.9 ft 5 / 1 = 0.4 ft. Total = = 1.4 ft Step 1 Since we want the surface area in square feet (ft ), we need to change all measurements to feet Divide the inches ( ) measurement by 1 and add it to the feet measurement ( )

16 Christmas time is approaching and you have purchased the same gift for each of your 14 co-workers. The gifts are packaged in boxes with dimensions by 1 5 by If there are 80 square feet of wrapping paper per roll, how many rolls of wrapping paper do you require to wrap all your gifts?.17 ft l 1.9 ft h 1.4 ft w Step Calculate the surface area of one gift A = lw + lh + wh = (.17)(1.4) + (.17)(1.9) + (1.4)(1.9) = = ft (or square feet) Since there area 14 people = ft

17 Christmas time is approaching and you have purchased the same gift for each of your 14 co-workers. The gifts are packaged in boxes with dimensions by 1 5 by If there are 80 square feet of wrapping paper per roll, how many rolls of wrapping paper do you require to wrap all your gifts?.17 ft 1.9 ft 1.4 ft Step 3 Determine how many rolls are required to wrap gifts for 14 people Since one roll covers 80 ft... # of rolls = Total surface area / area per roll = ft / 80 ft = 3.5 rolls Therefore 4 rolls should be purchased to cover the presents

18 ASSIGNMENT 1. Determine the surface area of the following prisms: (a) (b). You have been asked to paint a room that is 15 long, 11 wide. The paint can indicates that 1 gallon of paint will cover 50m. How many cans must be purchased if you must apply two coats of paint and the walls are 10 high? (Note: The ceiling and floor will not be painted) Include a net with your solution.

19 Homework pg (Day 1) #1 to 6 (Day ) 7 to 9, 11

Surface Area of Prisms

Surface 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 information

In Problems #1 - #4, find the surface area and volume of each prism.

In 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 information

Surface Area Quick Review: CH 5

Surface Area Quick Review: CH 5 I hope you had an exceptional Christmas Break.. Now it's time to learn some more math!! :) Surface Area Quick Review: CH 5 Find the surface area of each of these shapes: 8 cm 12 cm 4cm 11 cm 7 cm Find

More information

SURFACE AREA AND VOLUME

SURFACE 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 information

17.2 Surface Area of Prisms and Cylinders

17.2 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 information

Chapter 1 Measurement

Chapter 1 Measurement Chapter 1 Measurement Math 1201 1 Chapter 1 Measurement Sections 1.1-1.3: Goals: Converting between imperial units by unit analysis Converting between SI units Converting between SI and imperial units

More information

Area of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in

Area 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 information

Basic Math for the Small Public Water Systems Operator

Basic 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 information

Finding Volume of Rectangular Prisms

Finding 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 three-dimensional composite shapes.

More information

3D Geometry: Chapter Questions

3D Geometry: Chapter Questions 3D Geometry: Chapter Questions 1. What are the similarities and differences between prisms and pyramids? 2. How are polyhedrons named? 3. How do you find the cross-section of 3-Dimensional figures? 4.

More information

Name: Date: Geometry Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Solid Geometry. Name: Teacher: Pd: Name: Date: Geometry 2012-2013 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-7 HW: Pgs: 8-10 DAY 2: SWBAT: Calculate the Volume of

More information

6.3. Surface Area of Solids The Gift Box. My Notes ACTIVITY

6.3. Surface Area of Solids The Gift Box. My Notes ACTIVITY Surface Area of Solids SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge J.T. is the creative director for a paper products company. The company is introducing a new line of gift boxes, called

More information

Perimeter, Area, and Volume

Perimeter, 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 information

Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference

Grade 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 information

Geometry Review. Here are some formulas and concepts that you will need to review before working on the practice exam.

Geometry Review. Here are some formulas and concepts that you will need to review before working on the practice exam. Geometry Review Here are some formulas and concepts that you will need to review before working on the practice eam. Triangles o Perimeter or the distance around the triangle is found by adding all of

More information

Area of Parallelograms (pages 546 549)

Area 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 information

Grade 11 Essential Mathematics Unit 6: Measurement and Geometry

Grade 11 Essential Mathematics Unit 6: Measurement and Geometry Grade 11 Essential Mathematics Unit 6: 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

More information

SA 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

SA 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 information

Topic 9: Surface Area

Topic 9: Surface Area Topic 9: Surface Area for use after Covering and Surrounding (Investigation 5) Jillian is wrapping a box of model cars for her brother s birthday. Jillian needs to measure the box to see if she has enough

More information

GAP CLOSING. Volume and Surface Area. Intermediate / Senior Student Book

GAP 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 information

Geometry Notes VOLUME AND SURFACE AREA

Geometry 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 information

CC Investigation 4: Measurement

CC Investigation 4: Measurement Content Standards 6.G., 6.G. CC Investigation : Measurement Mathematical Goals At a Glance PACING 3 days DOMAIN: Geometry Find the volume of a right rectangular prism with fractional edge lengths by packing

More information

Area Long-Term Memory Review Review 1

Area Long-Term 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 information

Right Prisms Let s find the surface area of the right prism given in Figure 44.1. Figure 44.1

Right 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 information

Solids. Objective A: Volume of a Solids

Solids. 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 information

CONNECT: Volume, Surface Area

CONNECT: 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 information

Junior Math Circles March 10, D Geometry II

Junior Math Circles March 10, D Geometry II 1 University of Waterloo Faculty of Mathematics Junior Math Circles March 10, 2010 3D Geometry II Centre for Education in Mathematics and Computing Opening Problem Three tennis ball are packed in a cylinder.

More information

VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

VOLUME 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 information

Solutions Section J: Perimeter and Area

Solutions Section J: Perimeter and Area Solutions Section J: Perimeter and Area 1. The 6 by 10 rectangle below has semi-circles attached on each end. 6 10 a) Find the perimeter of (the distance around) the figure above. b) Find the area enclosed

More information

B = 1 14 12 = 84 in2. Since h = 20 in then the total volume is. V = 84 20 = 1680 in 3

B = 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 two-dimensional 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 information

Module: Mathematical Reasoning

Module: Mathematical Reasoning Module: Mathematical Reasoning Lesson Title: Using Nets for Finding Surface Area Objectives and Standards Students will: Draw and construct nets for 3-D objects. Determine the surface area of rectangular

More information

Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.

Show 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 information

Area 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 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 information

Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area 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 information

Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd: Name: Date: Geometry Honors 2013-2014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-6 HW: Pgs: 7-10 DAY 2: SWBAT: Calculate the Volume

More information

Surface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry

Surface 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 information

Characteristics of the Four Main Geometrical Figures

Characteristics 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 information

Geometry Notes PERIMETER AND AREA

Geometry 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 information

Line AB (no Endpoints) Ray with Endpoint A. Line Segments with Endpoints A and B. Angle is formed by TWO Rays with a common Endpoint.

Line AB (no Endpoints) Ray with Endpoint A. Line Segments with Endpoints A and B. Angle is formed by TWO Rays with a common Endpoint. Section 8 1 Lines and Angles Point is a specific location in space.. Line is a straight path (infinite number of points). Line Segment is part of a line between TWO points. Ray is part of the line that

More information

1 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

1 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 information

Area, Perimeter, Volume and Pythagorean Theorem Assessment

Area, Perimeter, Volume and Pythagorean Theorem Assessment Area, Perimeter, Volume and Pythagorean Theorem Assessment Name: 1. Find the perimeter of a right triangle with legs measuring 10 inches and 24 inches a. 34 inches b. 60 inches c. 120 inches d. 240 inches

More information

10-4 Surface Area of Prisms and Cylinders

10-4 Surface Area of Prisms and Cylinders : Finding Lateral Areas and Surface Areas of Prisms 2. Find the lateral area and surface area of the right rectangular prism. : Finding Lateral Areas and Surface Areas of Right Cylinders 3. Find the lateral

More information

A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height

A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side

More information

1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?

1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack? Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is

More information

Sect 9.5 - Perimeters and Areas of Polygons

Sect 9.5 - Perimeters and Areas of Polygons Sect 9.5 - Perimeters and Areas of Polygons Ojective a: Understanding Perimeters of Polygons. The Perimeter is the length around the outside of a closed two - dimensional figure. For a polygon, the perimeter

More information

3Surface Area, Volume, and Capacity

3Surface Area, Volume, and Capacity 124 Chapter 3Surface Area, Volume, and Capacity How much water do you think this water tank can hold? What would you need to know to calculate the exact amount? 3.1 Surface Area of Prisms REVIEW: WORKING

More information

Mensuration Introduction

Mensuration Introduction Mensuration Introduction Mensuration is the process of measuring and calculating with measurements. Mensuration deals with the determination of length, area, or volume Measurement Types The basic measurement

More information

Integrated Algebra: Geometry

Integrated 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 information

Pizza! Pizza! Assessment

Pizza! 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 information

Geometry Chapter 12. Volume. Surface Area. Similar shapes ratio area & volume

Geometry Chapter 12. Volume. Surface Area. Similar shapes ratio area & volume Geometry Chapter 12 Volume Surface Area Similar shapes ratio area & volume Date Due Section Topics Assignment Written Exercises 12.1 Prisms Altitude Lateral Faces/Edges Right vs. Oblique Cylinders 12.3

More information

Imperial Measures of Length

Imperial Measures of Length SI system of measures: Imperial Measures of Length is an abbreviation for a system of units based on powers of 10; the fundamental unit: of length is the ; of mass is the ; and of time is the. Imperial

More information

Lesson 7: Using Formulas

Lesson 7: Using Formulas Lesson 7: Using Formulas Steps for Solving Problems Using a Formula 1. 2. 3. 4. Example 1 Using the formula: Density = mass/volume or D = m/v Find the density of a rock that has a volume of 20 ml with

More information

*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.

*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle. Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the

More information

Chapter 1.3 and 1.4 Practice Quiz

Chapter 1.3 and 1.4 Practice Quiz Name: Class: _ Date: _ Chapter 1.3 and 1.4 Practice Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. 1. This composite object is made using centimetre

More information

Fundamentals of Geometry

Fundamentals 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 information

Surface Area of Prisms

Surface Area of Prisms Surface Area of Prisms Jen Kershaw Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content,

More information

Unit 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. 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 information

12-4 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

12-4 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 information

Name: Class: Date: Geometry Chapter 3 Review

Name: Class: Date: Geometry Chapter 3 Review Name: Class: Date: ID: A Geometry Chapter 3 Review. 1. The area of a rectangular field is 6800 square meters. If the width of the field is 80 meters, what is the perimeter of the field? Draw a diagram

More information

Grade 7/8 Math Circles Winter D Geometry

Grade 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 information

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!

YOU 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 information

Demystifying Surface Area and Volume Teachers Edition

Demystifying Surface Area and Volume Teachers Edition Demystifying Surface and Volume Teachers Edition These constructions and worksheets can be done in pairs, small groups or individually. Also, may use as guided notes and done together with teacher. CYLINDER

More information

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism.

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism. Find the volume of each prism. 3. the oblique rectangular prism shown at the right 1. The volume V of a prism is V = Bh, where B is the area of a base and h is the height of the prism. If two solids have

More information

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 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 information

Area of Circles. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and record in the blanks above.

Area of Circles. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and record in the blanks above. Name: Area of Circles Label: Length: Label: Length: A Part 1 1. Label the diameter and radius of Circle A. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and recd

More information

Covering and Surrounding: Homework Examples from ACE

Covering and Surrounding: Homework Examples from ACE Covering and Surrounding: Homework Examples from ACE Investigation 1: Extending and Building on Area and Perimeter, ACE #4, #6, #17 Investigation 2: Measuring Triangles, ACE #4, #9, #12 Investigation 3:

More information

Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min. Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.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 information

Name Date Period. 3D Geometry Project

Name Date Period. 3D Geometry Project Name 3D Geometry Project Part I: Exploring Three-Dimensional Shapes In the first part of this WebQuest, you will be exploring what three-dimensional (3D) objects are, how to classify them, and several

More information

Calculating Area, Perimeter and Volume

Calculating 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 information

CONNECT: Volume, Surface Area

CONNECT: Volume, Surface Area CONNECT: Volume, Surface Area 1. VOLUMES OF SOLIDS A solid is a three-dimensional (3D) object, that is, it has length, width and height. One of these dimensions is sometimes called thickness or depth.

More information

Filling and Wrapping: Homework Examples from ACE

Filling and Wrapping: Homework Examples from ACE Filling and Wrapping: Homework Examples from ACE Investigation 1: Building Smart Boxes: Rectangular Prisms, ACE #3 Investigation 2: Polygonal Prisms, ACE #12 Investigation 3: Area and Circumference of

More information

Lesson 3.2 Perfect Squares, Perfect Cubes, and Their Roots Exercises (pages )

Lesson 3.2 Perfect Squares, Perfect Cubes, and Their Roots Exercises (pages ) Lesson. Perfect Squares, Perfect Cubes, and Their Roots Exercises (pages 146 147) A 4. Use a calculator to write each number as a product of its prime factors, then arrange the factors in equal groups.

More information

Rugs. This problem gives you the chance to: find perimeters of shapes use Pythagoras Rule. Hank works at a factory that makes rugs.

Rugs. This problem gives you the chance to: find perimeters of shapes use Pythagoras Rule. Hank works at a factory that makes rugs. Rugs This problem gives you the chance to: find perimeters of shapes use Pythagoras Rule Hank works at a factory that makes rugs. The edge of each rug is bound with braid. Hank s job is to cut the correct

More information

5. Surface Area Practice Chapter Test

5. Surface Area Practice Chapter Test ID: A Date: / / Name: Block ID: 5. Surface Area Practice Chapter Test Multiple Choice Identify the choice that best completes the statement or answers the question. Choose the best answer. 1. Which combination

More information

Geo - CH10 Practice Test

Geo - CH10 Practice Test Geo - H10 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. lassify the figure. Name the vertices, edges, and base. a. triangular pyramid vertices:,,,,

More information

12-2 Surface Areas of Prisms and Cylinders. 1. Find the lateral area of the prism. SOLUTION: ANSWER: in 2

12-2 Surface Areas of Prisms and Cylinders. 1. Find the lateral area of the prism. SOLUTION: ANSWER: in 2 1. Find the lateral area of the prism. 3. The base of the prism is a right triangle with the legs 8 ft and 6 ft long. Use the Pythagorean Theorem to find the length of the hypotenuse of the base. 112.5

More information

12 Surface Area and Volume

12 Surface Area and Volume 12 Surface Area and Volume 12.1 Three-Dimensional 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 information

5.2. Nets and Solids LESSON. Vocabulary. Explore. Materials

5.2. Nets and Solids LESSON. Vocabulary. Explore. Materials LESSON 5.2 Nets and Solids A net is a flat figure that can be folded to form a closed, three- dimensional object. This type of object is called a geometric solid. Inv 1 Use a Net 229 Inv 2 Use Nets to

More information

Platonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:

Platonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples: Solid Geometry Solid Geometry is the geometry of three-dimensional space, the kind of space we live in. Three Dimensions It is called three-dimensional or 3D because there are three dimensions: width,

More information

Name: School Team: X = 5 X = 25 X = 40 X = 0.09 X = 15

Name: School Team: X = 5 X = 25 X = 40 X = 0.09 X = 15 7th/8th grade Math Meet Name: School Team: Event : Problem Solving (no calculators) Part : Computation ( pts. each) ) / + /x + /0 = X = 5 ) 0% of 5 = x % of X = 5 ) 00 - x = ()()(4) + 6 X = 40 4) 0.6 x

More information

TERRA Environmental Research Institute

TERRA Environmental Research Institute TERR Environmental Research Institute MTHEMTIS FT PRTIE STRN 2 Measurement Perimeter and rea ircumference and rea of ircles Surface rea Volume Time, Weight/Mass, apacity, and Temperature SUNSHINE STTE

More information

Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.

Height. 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 information

Perimeter. 14ft. 5ft. 11ft.

Perimeter. 14ft. 5ft. 11ft. Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine

More information

S.A. = L.A. + 2B = ph + 2B

S.A. = L.A. + 2B = ph + 2B Page 1 of 5 View Tutorial 5c Objective: Find the lateral area, total surface area, and volume of rectangular prisms. A prism is a polyhedron with two congruent & parallel bases. The other faces are the

More information

Perfume 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. 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 cost-efficient box. The Persuasive perfume bottle is in the shape of a regular hexagonal prism 10 centimeters

More information

Scaling Three-Dimensional Figures

Scaling Three-Dimensional Figures exploration Scaling Three-Dimensional Figures A rectangular box can be scaled up by increasing one of its three dimensions. To increase one dimension of the box, multiply the dimension by a scale factor.

More information

11-1. Space Figures and Cross Sections. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary

11-1. Space Figures and Cross Sections. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary 11-1 Space Figures and Cross Sections Vocabulary Review Complete each statement with the correct word from the list. edge edges vertex vertices 1. A(n) 9 is a segment that is formed by the intersections

More information

Precision and Measurement

Precision and Measurement NAME DATE PERIOD Precision and Measurement The precision or exactness of a measurement depends on the unit of measure. The precision unit is the smallest unit on a measuring tool. Significant digits include

More information

Measuring Prisms and Cylinders. Suggested Time: 5 Weeks

Measuring Prisms and Cylinders. Suggested Time: 5 Weeks Measuring Prisms and Cylinders Suggested Time: 5 Weeks Unit Overview Focus and Context In this unit, students will use two-dimensional nets to create threedimensional solids. They will begin to calculate

More information

Section 2.4: Applications and Writing Functions

Section 2.4: Applications and Writing Functions CHAPTER 2 Polynomial and Rational Functions Section 2.4: Applications and Writing Functions Setting up Functions to Solve Applied Problems Maximum or Minimum Value of a Quadratic Function Setting up Functions

More information

Sect 8.3 Quadrilaterals, Perimeter, and Area

Sect 8.3 Quadrilaterals, Perimeter, and Area 186 Sect 8.3 Quadrilaterals, Perimeter, and Area Objective a: Quadrilaterals Parallelogram Rectangle Square Rhombus Trapezoid A B E F I J M N Q R C D AB CD AC BD AB = CD AC = BD m A = m D m B = m C G H

More information

Area is a measure of how much space is occupied by a figure. 1cm 1cm

Area 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 information

Functional Skills Mathematics

Functional Skills Mathematics Functional Skills Mathematics Level Learning Resource Perimeter and Area MSS1/L.7 Contents Perimeter and Circumference MSS1/L.7 Pages 3-6 Finding the Area of Regular Shapes MSS1/L.7 Page 7-10 Finding the

More information

Radius and Diameter of Circles (A)

Radius and Diameter of Circles (A) Radius and Diameter of Circles (A) C=40.841 ft C=57.805 mm C=15.708 ft C=33.929 cm Radius and Diameter of Circles (A) Answers C=40.841 ft C=57.805 mm 6.5 ft 9.2 mm 13.0 ft 18.4 mm C=15.708 ft C=33.929

More information

12-8 Congruent and Similar Solids

12-8 Congruent and Similar Solids Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. 3. Two similar cylinders have radii of 15 inches and 6 inches. What is the ratio

More information

Geometry: Chapter Questions. 1. How is the formula for area of a parallelogram related to area of a rectangle?

Geometry: Chapter Questions. 1. How is the formula for area of a parallelogram related to area of a rectangle? Geometry: Chapter Questions. How is the formula for area of a parallelogram related to area of a rectangle?. How is the formula for area of a triangle related to area of a rectangle?. How do you find the

More information

Student Name. Form REL. Mathematics II Geometry/Algebra II/Statistics. Released Items EDUCATION. Georgia Department of Education All Rights Reserved.

Student Name. Form REL. Mathematics II Geometry/Algebra II/Statistics. Released Items EDUCATION. Georgia Department of Education All Rights Reserved. Student ame Form REL Mathematics II Geometry/Algebra II/Statistics Released Items GEOR GIA DEPARTMET OF EDUCATIO Georgia Department of Education All Rights Reserved. Mathematics II Formula Sheet Below

More information

Perimeter is the length of the boundary of a two dimensional figure.

Perimeter is the length of the boundary of a two dimensional figure. Section 2.2: Perimeter and Area Perimeter is the length of the boundary of a two dimensional figure. The perimeter of a circle is called the circumference. The perimeter of any two dimensional figure whose

More information

Surface Area and Volume

Surface Area and Volume UNIT 7 Surface Area and Volume Managers of companies that produce food products must decide how to package their goods, which is not as simple as you might think. Many factors play into the decision of

More information

Prisms and Cylinders 3.1. In Investigation 2, you found the volume of rectangular prisms by filling. Filling Fancy Boxes

Prisms and Cylinders 3.1. In Investigation 2, you found the volume of rectangular prisms by filling. Filling Fancy Boxes ! s and Cylinders In Investigation 2, you found the volume of rectangular prisms by filling the prism with cubes. The number of cubes in the bottom layer is the same as the area of the rectangular base

More information