1.2. Volume. 18 MHR Chapter 1. sphere cylinder rectangular prism triangular prism

Size: px
Start display at page:

Download "1.2. Volume. 18 MHR Chapter 1. sphere cylinder rectangular prism triangular prism"

Transcription

1 1.2 Volume When designing a building, it is important for the architect to measure carefully so that the structure functions properly and is pleasing to the eye. Look at the buildings in the photograph. What geometric shapes can you identify? What problems could arise if incorrect measurements are used in constructing these shapes? sphere cylinder rectangular prism triangular prism Research the Internet for at least three cities or places with buildings or structures that have geometric shapes. Provide an image of each structure and indicate what geometric shapes are used. Which structures are made up of two or more different three-dimensional figures? What threedimensional figures are used to make up each structure? 18 MHR Chapter 1 01_FFCM12_CH1.indd 18 3/6/09 12:17:22 PM

2 Example 1 Volume of a Prism Determine the volume of concrete needed to construct the ramp shown, to the nearest tenth of a cubic metre. 1.2 m 2.5 m 45.0 cm Literacy Connect The base of a prism refers to one of the two congruent, parallel polygon sides. Depending on the orientation of the prism, the bases can be on the top and bottom, the front and back, or the left and right sides. Solution The ramp is in the shape of a triangular-based prism. Determine the area of the triangular base cm 2.5 m A = _ 1 (b h) 2 = _ 1 ( ) 45 cm = 0.45 m 2 = The base area of the prism is m 2. Multiply this value by the depth of the prism to determine its volume. 1.2 m 45.0 cm m 2 Volume = Base area Depth = = Approximately 0.7 m 3 of concrete is needed to construct the ramp. 1.2 Volume MHR 19 01_FFCM12_CH1.indd 19 3/6/09 12:17:23 PM

3 Example 2 Volume of a Cylinder A cylindrical container is to be planted with flowers. The container is be 2 ft high, and must hold 1.5 m 3 of soil. What is the minimum diameter, to the nearest centimetre? Solution Convert the height to metres. 1 ft = m = The height is m. Substitute h = and V = 1.5 into the formula for volume of a cylinder and solve for the radius. Method 1: Substitute, then rearrange. V = πr 2 h 1.5 = πr 2 (0.6096) 1.5 = πr 2 _ π = _ πr2 Divide both sides by π π r = r 2 Take the square root of both sides r Method 2: Rearrange, then substitute. V = πr 2 h V_ πh = _ πr2 h πh V_ πh = r 2 r = V_ πh r = 1.5 π(2) r V = 1.5 m 3 Divide both sides by πh. Take the square root of both sides. Substitute the values of V and h. Determine the minimum diameter. d = 2r = 2(0.885) = 1.77 The minimum diameter of the container is 1.77 m or 177 cm. h = 2 ft 20 MHR Chapter 1 01_FFCM12_CH1.indd 20 3/6/09 12:17:23 PM

4 Example 3 Volume of a Composite Figure Determine the volume, to two decimal places, of concrete needed to construct this staircase. 0.9 m 45 cm Solution This staircase is in the shape of a prism with a staircase-shaped base. Determine the area of the base and then multiply by the depth. Method 1: Use components. The base consists of six congruent squares = 1350 The total base area is 1350 cm 2. Multiply the base area by the depth to determine the volume of the prism. 0.9 m 1350 cm 2 Volume = Base area Depth = = Convert the base area to square metres: 1350 cm 2 ( ) = m 2. The volume of concrete needed to construct the staircase is approximately 0.24 m Volume MHR 21 01_FFCM12_CH1.indd 21 3/6/09 12:17:24 PM

5 Method 2: Use the volume of a simpler object. Think of the staircase as part of a larger square-based prism. The staircase consists of six of the nine congruent rows of cubes shown. The volume of the staircase is _ 6 9 or _ 2 the volume of the square-based prism. 3 Volume = _ 2 (Base area Depth) 3 = _ 2 3 ( ) = _ 2 3 (0.3645) = Convert 45 cm to 0.45 m and substitute. The volume of concrete needed to construct the staircase is 0.24 m 3. Key Concepts To apply a volume formula, all measures must be in common units. The volume of a prism, V, can be calculated by multiplying its base area by its height or depth. V = Base Area Depth or V = Base Area Height The volume of a cylinder can be calculated using the formula V = πr 2 h. Discuss the Concepts D1. a) What distinguishes a prism from other three-dimensional objects? b) Sketch three different prisms and identify them by the shapes of their bases. D2. a) Can a cylinder be thought of as a prism? Explain. b) Explain how the formula for the volume of a cylinder can be found by applying the relationship: V = Base area Depth or Height D3. Describe the steps 12 m you would follow to calculate the volume of this storage tank. 15 ft 22 MHR Chapter 1 01_FFCM12_CH1.indd 22 3/6/09 12:17:24 PM

6 Practise A 1. a) Identify the shape of the base of this prism. b) The base area of the prism is 25 cm 2 and its height is 4 cm. Determine the volume of the prism. 2. a) Which units would you use for the volume of this square-based prism? Explain. b) Calculate the volume of the prism. 12 cm 25 mm 3. Refer to the prism in question 2. Could this prism be described as a rectangular-based prism? Explain, using words and diagrams. Reasoning and Proving Representing Selecting Tools Problem Solving Connecting Reflecting Communicating 4. A cylinder has diameter 6.2 cm and height 11.4 cm. a) Sketch and label a diagram of the cylinder. b) Determine the volume of the cylinder to the nearest cubic centimetre. c) What volume of liquid will this cylinder hold, to two decimal places? Recall 1 L = 1000 cm 3. Apply B 5. Determine the volume of Fido s doghouse. 1.5 m Fido 2.0 m 1.0 m 1.4 m 1.2 Volume MHR 23 01_FFCM12_CH1.indd 23 3/6/09 12:17:25 PM

7 Reasoning and Proving Representing Selecting Tools Problem Solving Connecting Reflecting 6. A hockey puck has a diameter of 3 in. and height of 1 in. A cylindrical container holds a stack of four pucks. What is the minimum volume of this container, to the nearest cubic centimetre? Communicating 7. A cylinder has a circumference of 40 cm and a volume of 500 cm 3. Determine the height of the cylinder to the nearest tenth of a centimetre. 8. The volume of this package is 150 cm 3. 6 cm x 5 cm Determine the length of the package. Achievement Check 9. Abdi works in the forestry industry. His truck can carry 21 logs, stacked as shown. Each log has an average length of approximately 15 m and an average circumference of approximately 2 m. M12 V3F a) Determine the total volume of wood Abdi can haul in one load to the nearest cubic metre. b) What assumptions did you make? 24 MHR Chapter 1 01_FFCM12_CH1.indd 24 3/6/09 12:17:25 PM

8 10. a) Identify an object in your classroom or in a room at home that is in the shape of a prism. Sketch the object and label it with its measures. b) Determine the volume of the object. 11. Repeat question 10 for a prism with a base that is a composite figure. Extend C 12. Airplane fuel tanks are often located in the aircraft s wings. To fit inside the wing without any wasted space, some fuel tanks are designed in the shape of cylindrical prisms whose ends are ovals (ellipses) rather than circles. b a d The formula for the area of an ellipse is A = πab. The wing of an aircraft can accommodate an ellipse with a = 120 cm and b = 50 cm. a) Determine the depth, d, of the tank if it has to hold 200 L of fuel. b) How is the formula for the area of an ellipse related to the formula for the area of a circle? Explain. 13. Charlene is reading a book that has a volume of 120 in. 3, and cover dimensions of 8 in. by 10 in., as shown. The front and back covers are each 0.5 cm thick and each page is 0.05 mm thick. Charlene can read 20 pages per hour. Determine how many hours it will take for Charlene to read the entire book. 8 in. 10 in. 1.2 Volume MHR 25 01_FFCM12_CH1.indd 25 3/6/09 12:17:26 PM

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

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

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

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

Volume of a Cylinder

Volume of a Cylinder Volume of a Cylinder Focus on After this lesson, you will be able to φ determine the volume of a cylinder How much water do you use? You might be surprised. The water storage tank shown has a height of

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

1.6. Analyse Optimum Volume and Surface Area. Maximum Volume for a Given Surface Area. Example 1. Solution

1.6. Analyse Optimum Volume and Surface Area. Maximum Volume for a Given Surface Area. Example 1. Solution 1.6 Analyse Optimum Volume and Surface Area Estimation and oter informal metods of optimizing measures suc as surface area and volume often lead to reasonable solutions suc as te design of te tent in tis

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

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

Minimize the Surface Area of a Square-Based Prism

Minimize the Surface Area of a Square-Based Prism 9.3 Minimize the Surface Area of a Square-Based Prism The boxes used in packaging come in many shapes and sizes. A package must be suitable for the product, visually appealing, and cost efficient. Many

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

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

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

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

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

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

What You ll Learn. Why It s Important

What You ll Learn. Why It s Important These students are setting up a tent. How do the students know how to set up the tent? How is the shape of the tent created? How could students find the amount of material needed to make the tent? Why

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

1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this intersection?

1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed from this intersection? Student Name: Teacher: Date: District: Description: Miami-Dade County Public Schools Geometry Topic 7: 3-Dimensional Shapes 1. A plane passes through the apex (top point) of a cone and then through its

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

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

GCSE Revision Notes Mathematics. Volume and Cylinders

GCSE Revision Notes Mathematics. Volume and Cylinders GCSE Revision Notes Mathematics Volume and Cylinders irevise.com 2014. All revision notes have been produced by mockness ltd for irevise.com. Email: info@irevise.com Copyrighted material. All rights reserved;

More information

CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

CHAPTER 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 information

Activity Set 4. Trainer Guide

Activity Set 4. Trainer Guide Geometry and Measurement of Solid Figures Activity Set 4 Trainer Guide Mid_SGe_04_TG Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development GEOMETRY AND MEASUREMENT OF SOLID FIGURES

More information

Area & Volume. 1. Surface Area to Volume Ratio

Area & Volume. 1. Surface Area to Volume Ratio 1 1. Surface Area to Volume Ratio Area & Volume For most cells, passage of all materials gases, food molecules, water, waste products, etc. in and out of the cell must occur through the plasma membrane.

More information

EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES. Maths Level 2. Chapter 5. Shape and space

EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES. Maths Level 2. Chapter 5. Shape and space Shape and space 5 EDEXCEL FUNCTIONAL SKILLS PILOT TEACHER S NOTES Maths Level 2 Chapter 5 Shape and space SECTION H 1 Perimeter 2 Area 3 Volume 4 2-D Representations of 3-D Objects 5 Remember what you

More information

CALCULATING THE AREA OF A FLOWER BED AND CALCULATING NUMBER OF PLANTS NEEDED

CALCULATING THE AREA OF A FLOWER BED AND CALCULATING NUMBER OF PLANTS NEEDED This resource has been produced as a result of a grant awarded by LSIS. The grant was made available through the Skills for Life Support Programme in 2010. The resource has been developed by (managers

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

Cylinder Volume Lesson Plan

Cylinder Volume Lesson Plan Cylinder Volume Lesson Plan Concept/principle to be demonstrated: This lesson will demonstrate the relationship between the diameter of a circle and its circumference, and impact on area. The simplest

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

GCSE Exam Questions on Volume Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice.

GCSE Exam Questions on Volume Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice. Question 1. (AQA June 2003 Intermediate Paper 2 Calculator OK) A large carton contains 4 litres of orange juice. Cylindrical glasses of height 10 cm and radius 3 cm are to be filled from the carton. How

More information

The teacher gives the student a ruler, shows her the shape below and asks the student to calculate the shape s area.

The teacher gives the student a ruler, shows her the shape below and asks the student to calculate the shape s area. Complex area Georgia is able to calculate the area of a complex shape by mentally separating the shape into familiar shapes. She is able to use her knowledge of the formula for the area of a rectangle

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

Measurement. Volume It All Stacks Up. Activity:

Measurement. Volume It All Stacks Up. Activity: Measurement Activity: TEKS: Overview: Materials: Grouping: Time: Volume It All Stacks Up (7.9) Measurement. The student solves application problems involving estimation and measurement. The student is

More information

ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC

ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC ALPERTON COMMUNITY SCHOOL MATHS FACULTY ACHIEVING GRADE A/A* EXAM PRACTICE BY TOPIC WEEK Calculator paper Each set of questions is followed by solutions so you can check & mark your own work CONTENTS TOPIC

More information

How To Draw A Similar Figure From A Different Perspective

How To Draw A Similar Figure From A Different Perspective Chapter 6 Similarity of Figures 6.1 Similar Polygons 6.2 Determining if two Polygons are Similar 6.3 Drawing Similar Polygons 6.4 Similar Triangles 21 Name: 6.1 Similar Polygons A. What makes something

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

1 cm 3. 1 cm. 1 cubic centimetre. height or Volume = area of cross-section length length

1 cm 3. 1 cm. 1 cubic centimetre. height or Volume = area of cross-section length length Volume Many things are made in the shape of a cuboid, such as drink cartons and cereal boxes. This activity is about finding the volumes of cuboids. Information sheet The volume of an object is the amount

More information

Math 2201 Chapter 8 Review

Math 2201 Chapter 8 Review Olga Math 2201 Chapter 8 Review Multiple Choice 1. A 2 L carton of milk costs $3.26. What is the unit rate? a. $0.83/500 ml b. $3.27/2 L c. $0.61/L d. $1.63/L 2.. drove 346 km and used up 28.7 L of gas.

More information

12-1 Representations of Three-Dimensional Figures

12-1 Representations of Three-Dimensional Figures Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

More information

The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- Area = 1 2 D x d CIRCLE.

The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- Area = 1 2 D x d CIRCLE. Revision - Areas Chapter 8 Volumes The formulae for calculating the areas of quadrilaterals, circles and triangles should already be known :- SQUARE RECTANGE RHOMBUS KITE B dd d D D Area = 2 Area = x B

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

Lateral and Surface Area of Right Prisms

Lateral and Surface Area of Right Prisms CHAPTER A Lateral and Surface Area of Right Prisms c GOAL Calculate lateral area and surface area of right prisms. You will need a ruler a calculator Learn about the Math A prism is a polyhedron (solid

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

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

Unit 8 Angles, 2D and 3D shapes, perimeter and area

Unit 8 Angles, 2D and 3D shapes, perimeter and area Unit 8 Angles, 2D and 3D shapes, perimeter and area Five daily lessons Year 6 Spring term Recognise and estimate angles. Use a protractor to measure and draw acute and obtuse angles to Page 111 the nearest

More information

Think About This Situation

Think About This Situation Think About This Situation A popular game held at fairs or parties is the jelly bean guessing contest. Someone fills a jar or other large transparent container with a known quantity of jelly beans and

More information

PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY

PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY PIZZA! PIZZA! TEACHER S GUIDE and ANSWER KEY The Student Handout is page 11. Give this page to students as a separate sheet. Area of Circles and Squares Circumference and Perimeters Volume of Cylinders

More information

Chapter 4: Area, Perimeter, and Volume. Geometry Assessments

Chapter 4: Area, Perimeter, and Volume. Geometry Assessments Chapter 4: Area, Perimeter, and Volume Geometry Assessments Area, Perimeter, and Volume Introduction The performance tasks in this chapter focus on applying the properties of triangles and polygons to

More information

Geometry Solve real life and mathematical problems involving angle measure, area, surface area and volume.

Geometry Solve real life and mathematical problems involving angle measure, area, surface area and volume. Performance Assessment Task Pizza Crusts Grade 7 This task challenges a student to calculate area and perimeters of squares and rectangles and find circumference and area of a circle. Students must find

More information

CBA Volume: Student Sheet 1

CBA Volume: Student Sheet 1 CBA Volume: Student Sheet 1 For each problem, decide which cube building has more room inside, or if they have the same amount of room. Then find two ways to use cubes to check your answers, one way that

More information

WORK SCHEDULE: MATHEMATICS 2007

WORK SCHEDULE: MATHEMATICS 2007 , K WORK SCHEDULE: MATHEMATICS 00 GRADE MODULE TERM... LO NUMBERS, OPERATIONS AND RELATIONSHIPS able to recognise, represent numbers and their relationships, and to count, estimate, calculate and check

More information

CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.

CHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder. TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE 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 information

ACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.

ACTIVITY: 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 information

8.9 Intersection of Lines and Conics

8.9 Intersection of Lines and Conics 8.9 Intersection of Lines and Conics The centre circle of a hockey rink has a radius of 4.5 m. A diameter of the centre circle lies on the centre red line. centre (red) line centre circle INVESTIGATE &

More information

Chapter 8 Geometry We will discuss following concepts in this chapter.

Chapter 8 Geometry We will discuss following concepts in this chapter. Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles

More information

By the end of this set of exercises, you should be able to:

By the end of this set of exercises, you should be able to: BASIC GEOMETRIC PROPERTIES By the end of this set of exercises, you should be able to: find the area of a simple composite shape find the volume of a cube or a cuboid find the area and circumference of

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

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

Surfa Surf ce ace Area Area What You Will Learn

Surfa Surf ce ace Area Area What You Will Learn Surface Area A skyline is a view of the outline of buildings or mountains shown on the horizon. You can see skylines during the day or at night, all over the world. Many cities have beautiful skylines.

More information

2nd Semester Geometry Final Exam Review

2nd 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 information

Calculating the Surface Area of a Cylinder

Calculating the Surface Area of a Cylinder Calculating the Measurement Calculating The Surface Area of a Cylinder PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping

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

Overview. Essential Questions. Grade 8 Mathematics, Quarter 4, Unit 4.3 Finding Volume of Cones, Cylinders, and Spheres

Overview. Essential Questions. Grade 8 Mathematics, Quarter 4, Unit 4.3 Finding Volume of Cones, Cylinders, and Spheres Cylinders, and Spheres Number of instruction days: 6 8 Overview Content to Be Learned Evaluate the cube root of small perfect cubes. Simplify problems using the formulas for the volumes of cones, cylinders,

More information

Unit 10 Grade 7 Volume of Right Prisms

Unit 10 Grade 7 Volume of Right Prisms Unit 10 Grade 7 Volume of Right Prisms Lesson Outline Big Picture Students will: develop and apply the formula: Volume = area of the base height to calculate volume of right prisms; understand the relationship

More information

Areas of Polygons. Goal. At-Home Help. 1. A hockey team chose this logo for their uniforms.

Areas of Polygons. Goal. At-Home Help. 1. A hockey team chose this logo for their uniforms. -NEM-WBAns-CH // : PM Page Areas of Polygons Estimate and measure the area of polygons.. A hockey team chose this logo for their uniforms. A grid is like an area ruler. Each full square on the grid has

More information

EMAT 6450 - Mathematics in Context

EMAT 6450 - Mathematics in Context Melissa Wilson EMAT 6450 - Mathematics in Context Course/Unit: Accelerated Coordinate Algebra/Analytic Geometry A for Unit 9, Circles and Volume (This unit corresponds to Unit 3 in Analytic Geometry. The

More information

Maximum and minimum problems. Information sheet. Think about

Maximum and minimum problems. Information sheet. Think about Maximum and minimum problems This activity is about using graphs to solve some maximum and minimum problems which occur in industry and in working life. The graphs can be drawn using a graphic calculator

More information

Convert between units of area and determine the scale factor of two similar figures.

Convert between units of area and determine the scale factor of two similar figures. CHAPTER 5 Units of Area c GOAL Convert between units of area and determine the scale factor of two. You will need a ruler centimetre grid paper a protractor a calculator Learn about the Math The area of

More information

Charlesworth School Year Group Maths Targets

Charlesworth School Year Group Maths Targets Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve

More information

Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

More information

2. A painted 2 x 2 x 2 cube is cut into 8 unit cubes. What fraction of the total surface area of the 8 small cubes is painted?

2. A painted 2 x 2 x 2 cube is cut into 8 unit cubes. What fraction of the total surface area of the 8 small cubes is painted? Black Surface Area and Volume (Note: when converting between length, volume, and mass, 1 cm 3 equals 1 ml 3, and 1 ml 3 equals 1 gram) 1. A rectangular container, 25 cm long, 18 cm wide, and 10 cm high,

More information

Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)

Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes) Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.

More information

VOLUME AND SURFACE AREAS OF SOLIDS

VOLUME AND SURFACE AREAS OF SOLIDS VOLUME AND SURFACE AREAS OF SOLIDS Q.1. Find the total surface area and volume of a rectangular solid (cuboid) measuring 1 m by 50 cm by 0.5 m. 50 1 Ans. Length of cuboid l = 1 m, Breadth of cuboid, b

More information

Geometry - Calculating Area and Perimeter

Geometry - Calculating Area and Perimeter Geometry - Calculating Area and Perimeter In order to complete any of mechanical trades assessments, you will need to memorize certain formulas. These are listed below: (The formulas for circle geometry

More information

Demystifying Surface Area and Volume

Demystifying Surface Area and Volume Demystifying Surface and Volume CYLINDER 1. Use the net of the cylinder provided. Measure in centimeters and record the radius of the circle, and the length and width of the rectangle. radius = length

More information

What You ll Learn. Why It s Important

What You ll Learn. Why It s Important What is a circle? Where do you see circles? What do you know about a circle? What might be useful to know about a circle? What You ll Learn Measure the radius, diameter, and circumference of a circle.

More information

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

More information

Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Unit 3 Practice Test. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: lass: ate: I: Unit 3 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. The radius, diameter, or circumference of a circle is given. Find

More information

Scale Factors and Volume. Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor

Scale Factors and Volume. Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor Scale Factors and Discovering the effect on the volume of a prism when its dimensions are multiplied by a scale factor Find the volume of each prism 1. 2. 15cm 14m 11m 24m 38cm 9cm V = 1,848m 3 V = 5,130cm

More information

Tallahassee Community College PERIMETER

Tallahassee 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 information

Ministry of Education. The Ontario Curriculum. Mathematics. Mathematics Transfer Course, Grade 9, Applied to Academic

Ministry of Education. The Ontario Curriculum. Mathematics. Mathematics Transfer Course, Grade 9, Applied to Academic Ministry of Education The Ontario Curriculum Mathematics Mathematics Transfer Course, Grade 9, Applied to Academic 2 0 0 6 Contents Introduction....................................................... 2

More information

IWCF United Kingdom Branch

IWCF United Kingdom Branch IWCF United Kingdom Branch Drilling Calculations Distance Learning Programme Part 2 Areas and Volumes IWCF UK Branch Distance Learning Programme - DRILLING CALCULATIONS Contents Introduction Training objectives

More information

In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

More information

numerical place value additional topics rounding off numbers power of numbers negative numbers addition with materials fundamentals

numerical place value additional topics rounding off numbers power of numbers negative numbers addition with materials fundamentals Math Scope & Sequence fundamentals number sense and numeration of the decimal system Count to 10 by units Associate number to numeral (1-10) KN 1 KN 1 KN 2 KN 2 Identify odd and even numbers/numerals and

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

10-3 Area of Parallelograms

10-3 Area of Parallelograms 0-3 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 information

6Geometry in Design. Key Terms

6Geometry in Design. Key Terms 6Geometry in Design Why is knowledge of geometry important for so many activities? Think about a concert that you attended. How did geometry influence the band who wrote the music, the craftspeople who

More information

Unit 15: Measurement Length, Area and Volume

Unit 15: Measurement Length, Area and Volume Unit 15: Measurement Length, Area and Volume Section A: Circumference measuring the circumference of a round object. You will to show all of your working out. C 5 d where: C 5 circumference 5 3.14 d 5

More information

ISAT Mathematics Performance Definitions Grade 4

ISAT Mathematics Performance Definitions Grade 4 ISAT Mathematics Performance Definitions Grade 4 EXCEEDS STANDARDS Fourth-grade students whose measured performance exceeds standards are able to identify, read, write, represent, and model whole numbers

More information

Math 10 - Unit 3 Final Review - Numbers

Math 10 - Unit 3 Final Review - Numbers Class: Date: Math 10 - Unit Final Review - Numbers Multiple Choice Identify the choice that best answers the question. 1. Write the prime factorization of 60. a. 2 7 9 b. 2 6 c. 2 2 7 d. 2 7 2. Write the

More information

WEIGHTS 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 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 information

Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem.

Sandia High School Geometry Second Semester FINAL EXAM. Mark the letter to the single, correct (or most accurate) answer to each problem. Sandia High School Geometry Second Semester FINL EXM Name: Mark the letter to the single, correct (or most accurate) answer to each problem.. What is the value of in the triangle on the right?.. 6. D.

More information

Area and Circumference

Area 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 information

MATH STUDENT BOOK. 6th Grade Unit 8

MATH STUDENT BOOK. 6th Grade Unit 8 MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF

More information

CAMI Education linked to CAPS: Mathematics

CAMI Education linked to CAPS: Mathematics - 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to

More information

MENSURATION. Definition

MENSURATION. Definition MENSURATION Definition 1. Mensuration : It is a branch of mathematics which deals with the lengths of lines, areas of surfaces and volumes of solids. 2. Plane Mensuration : It deals with the sides, perimeters

More information

Georgia Department of Education Georgia Standards of Excellence Framework GSE Grade 6 Mathematics Unit 5

Georgia Department of Education Georgia Standards of Excellence Framework GSE Grade 6 Mathematics Unit 5 **Volume and Cubes Back to Task Table In this problem-based task, students will examine the mathematical relationship between the volume of a rectangular prism in cubic units and the number of unit cubes

More information

14.1 Drum Roll, Please! Volume of a Cylinder... 747. 14.2 Piling On! Volume of a Cone...761. 14.3 All Bubbly. Volume of a Sphere...

14.1 Drum Roll, Please! Volume of a Cylinder... 747. 14.2 Piling On! Volume of a Cone...761. 14.3 All Bubbly. Volume of a Sphere... Volume Disco balls are spheres that reflect light in all different directions. They were really popular in dance clubs throughout the 1960s, 1970s, and 1980s. 14.1 Drum Roll, Please! Volume of a Cylinder...

More information