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

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.

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

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.

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

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.

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 cubic centimeters.

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?

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 cubic millimeters.

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.)

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.

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.)

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).

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.

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

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

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

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.

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