1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 5.5 Volume and Surface Area

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Understand the concept of volume. o Know the formulas for finding the volume of five geometric solids. o Understand the concept of surface area. o Know the formulas for finding the surface area of three geometric solids.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Formulas for Volume Five Geometric Solids and the Formulas for Their Volumes

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Finding the Volume of a Rectangular Solid Find the volume of the rectangular solid with length 8 in., width 4 in., and height 1 ft. Write your answer in cubic inches and in cubic feet.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Finding the Volume of a Rectangular Solid (cont.) Solution

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Volume of a Sphere Find the volume of a sphere with radius 9 cm.

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Finding the Volume of a Sphere (cont.) Solution Using the formula for the volume of a sphere: The volume of the sphere is 3052.08 cubic centimeters.

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Finding the Volume of a Cylinder What is the volume of a cylinder with a height of 10 mm and a circular base with a diameter of 8 mm?

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Finding the Volume of a Cylinder (cont.) Solution We know that the diameter is 8 mm but we need the radius. The radius is half of the diameter: So applying the formula for the volume of a cylinder, we have: The volume of the cylinder is 502.4 cubic millimeters.

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Volume of a Solid Find the volume of a solid with the dimensions indicated. (Use  = 3.14.)

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Volume of a Solid (cont.) Solution On top of the cylinder is a hemisphere (one-half of a sphere). Find the volume of the cylinder and hemisphere and add the results.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Finding the Volume of a Solid (cont.)

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Finding the Volume of a Cube Find the volume of a cube with s = 3 yards in both cubic yards and cubic feet. (1 yard = 3 feet).

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 5: Finding the Volume of a Cube (cont.) Solution We apply the formula V = s 3 twice; once by using s = 3 yards and once by using s = 9 feet. Notice that because feet are smaller than yards, there are many more cubic feet than cubic yards in the cube.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Formulas for Surface Area Three Geometric Solids and the Formulas for Their Surface Areas

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 6: Finding the Surface Area of a Rectangular Solid A cereal box in the shape of a rectangular solid has the following dimensions: l = 30 cm, w = 10 cm, h = 40 cm Find the surface area of the box. Solution

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 7: Finding the Surface Area of a Right Circular Cylinder A coffee can in the shape of a cylinder has the following dimensions: r = 2 in., h = 5 in. Find the surface area of the can. (Use  = 3.14.) Solution

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems 1.Find the volume of a rectangular pyramid with length 4.5 cm, width 3.2 cm, and height 1.6 cm. 2.A right circular cone has a height of 12 ft and a circular base with radius 6 ft. What is the volume of the cone? 3.A ball in the shape of a sphere has a diameter of 18 in. Air is blown into the ball until it has a new diameter of 20 in. What is the change in the volume of the ball? Round your answer to the hundredth place.

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1. 7.68 cm 3 2.452.16 ft 3 3.1134.59 in. 3