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

Geometry	Chapter 13

Lesson 13-1

Example 1  Volume of a Triangular Prism
Find the volume of the triangular prism.	
Use the Pythagorean Theorem to find the length of 
the base of the prism.
	a^2 + b^2	= c^2	Pythagorean Theorem
	a^2 + 24^2	= 25^2	b = 24, c = 25
	a^2 + 576	= 625	Multiply.
	a^2	= 49	Subtract 576 from each side.
	a	= 7	Take the square root of each side.

Next, find the volume of the prism.
V	= Bh	Volume of a prism
	= (7)(24)(16)	B = (7)(24), h = 16
	= 1344	Simplify.

The volume of the prism is 1344 cubic meters.

Example 2  Volume of a Rectangular Prism
STRUCTURES  The heaviest door in the world is a radiation shield door in the National Institute for Fusion Science at Toki, Japan. It is 38.5 feet high, 37.4 feet wide, and 6.6 feet thick. Its total weight is 708.6 tons. What is the weight of one cubic yard of the material used to make the door?
First, make a drawing. 	
To find the weight of one cubic yard of the material used, 
first find the volume of the door in cubic feet.

V	= Bh	Volume of a prism
	= (37.4)(6.6)(38.5)	B = (37.4)(6.6), h = 38.5
	= 9503.34	Simplify.

Now convert the volume in cubic feet to cubic yards. Since 1 yard = 3 feet, 
1 cubic yard = 3 • 3 • 3 or 27 cubic feet.
9503.34 cubic feet = (9503.34) ÷ 27 ≈ 352.0 cubic yards

Now divide the total weight of the door by the number of cubic yards.
 ≈ 2.0

The weight of one cubic yard of the material used to make the door is about 2 tons.

Example 3  Volume of a Cylinder
Find the volume of each cylinder.
a. 	The height h is 38.3 centimeters, and the radius r is 
11.7 centimeters.
	V	= πr^2h 		Volume of a cylinder
		= π(11.7)^2(38.3)	r = 11.7, h = 38.3
		≈ 16,471.0		Use a calculator.
	The volume is approximately 16,471.0 cubic centimeters.

b. 	The diameter of the base, the diagonal, and the lateral edge of the cylinder form a right triangle. Use the Pythagorean Theorem to find the height.
	a^2 + b^2	= c^2		Pythagorean Theorem
	h^2 + (45)^2	= (51)^2		a = h, b = 45, c = 51
	h^2 + 2025	= 2601		Multiply.
	h^2	= 576		Subtract 2025 from each side.
	h	= 24		Take the square root of each side.

	Now find the volume.
	V	= r^2h		Volume of a cylinder
	= (22.5)^2(24)		r = 22.5, h = 24
	≈ 38,170.4		Use a calculator.
	The volume is approximately 38,170.4 cubic feet.

Example 4  Volume of an Oblique Cylinder
Find the volume of the oblique cylinder.	
To find the volume, use the formula for a right cylinder.
V	= πr^2h	Volume of a cylinder
	= π(4.4)^2(13.2)	r = 4.4, h = 13.2
	≈ 802.8	Use a calculator.

The volume is approximately 802.8 cubic meters.