Title: Lesson 14-5
Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 8-7

For Examples 1-3 Find the Volume of Solids
a. Find the volume of the rectangular prism.

Estimate 
V ≈ 20 in. × 4 in. × 6 in. or 480 in^3

In the figure, the length is 18 inches, the width is 4 inches, and the height is 6 inches.	

METHOD 1 Use V = ℓwh.
V = ℓwh	Use the formula for the volume of rectangular prism.
V = 18 × 4 × 6	Substitute 18 for ℓ, 4 for w, and 6 for h.
V = 432	Multiply.
The volume is 432 cubic inches.

METHOD 2 Use V = Bh.
B, or the area of the base, is 18 × 4 or 72 square inches.
V = Bh	Use the formula for the volume of rectangular prism.
V = 72 × 6	Substitute 72 for B and 6 for h.
V = 432	Multiply.
The volume is 432 cubic inches.

Check for Reasonableness We overestimated our measurements. So, the answer should be less than the estimate. 432 < 480 ✓

b. Find the volume of the rectangular prism.

V = ℓwh	Use the formula for the volume of rectangular prism.
V = 	Substitute 6 for ℓ, 4 for w, and 3 for h.
V = 72	Multiply.

The volume is 72 cubic centimeters.

c. [Real-World Example] PACKAGING   A box used to ship textbooks is a rectangular prism. It has length 2.75 feet, width 2 feet, and height 1.5 feet. What is the approximate volume of the box?

To find the approximate volume of the box, estimate. You do not need an exact answer. First round the dimensions of the box to the nearest whole number.

2.75 ft ≈ 3 ft	2 ft = 2 ft	1.5 ft ≈ 2 ft

Then find the volume.

V = ℓwh		Use the formula for the volume of a rectangular prism.
V ≈ 3 × 2 × 2		Substitute 3 for ℓ, 2 for w, and 2 for h.
V ≈ 12				Multiply.	

The approximate volume of the box is 12 cubic feet.

d. Find the volume of the pyramid. Round to the nearest tenth.

V = 1/3Bh	Use the formula for the 		
	volume of a pyramid.

V = 1/3(1/2 · 2.5 · 3.2)10	Substitute known values. 
	B = 1/2 · 2.5 · 3.2, h = 10

V ≈ 13.3	Multiply.

The volume is about 13.3 cubic meters.

e. Find the volume of the cylinder. Use π = 3.14.
	
V = πr^2h		Use the formula for the volume of a cylinder
V = 3.14 · 4^2 · 10	Substitute.
V ≈ 502.7	Multiply. 

The volume is about 502.7 cubic feet.