Title: Example 1 Geometric Mean
Author: Tim Heppner
Last saved by: MHE
Company: MCGRAW-HILL

Geometry	Chapter 13

Lesson 13-3

Example 1  Volumes of Spheres
Find the volume of each sphere.

	V	= 4/3πr^3 	Volume of a sphere
	= 4/3π(6.7)^3 	r = 6.7
	≈ 1259.8 m^3	Use a calculator.

Example 2  Volume of a Hemisphere
Find the volume of the hemisphere.	
The volume of a hemisphere is one-half the volume of the sphere.
V	= 1/2	One half the volume of a sphere
	= 2/3π(27.5)^3	r = 27.5
	≈ 43,556.9 m^3	Use a calculator.

Example 3  Volume Comparison
Short Response Test Item

Compare the total volume of the two spheres and 	
the volume of the cylinder. Determine which 
quantity is greater.

Read the Test Item
You are asked to compare the total volume of the two spheres and the volume of the cylinder.

Solve the Test Item

Volume of the spheres:
	total volume	= volume 1 + volume 2
	V	= 4/3πr^3 + 4/3π
		= 4/3πr^3 + 1/6πr^3 
		= 3/2πr^3

Volume of the Cylinder:
V	= πr^2h
	= πr^2(3r)
	= 3πr^3

Compare 3/2πr^3 to 3πr^3. Since 3/2 = 1.5, 3 is twice as great as 3/2. So, the volume of the cylinder is twice the volume of the two spheres.