Basic Mathematics for College Students

804 Chapter 9 An Introduction to Geometry

6 m

9 m

6 m

EXAMPLE (^4) Find the volume of the pyramid shown
on the right.
StrategyFirst, we will find the area of the square
base of the pyramid.
WHYThe volume of a pyramid is of the product of
the area of its base and its height.
SolutionSince the base is a square with each side
6 meters long, the area of the base is (6 m)^2 , or 36 m^2. To find the volume of the
pyramid, we proceed as follows:
This is the formula for the volume of a pyramid.
Substitute 36 for B,the area of the base, and 9 for h,the height.
Multiply:.
Complete the multiplication.
The volume of the pyramid is 108 m^3.

 108

1

3 (36)

36

12(9) 3  12

V

1

3

( 36 )( 9 )

V

1

3

Bh

13

Self Check 4

Find the volume of the pyramid

shown below.

Now TryProblem 37

12 cm

16 cm

20 cm

2 Find the volume of cylinders, cones, and spheres.

EXAMPLE (^5) Find the volume of the cylinder shown on the
right. Give the exact answer and an approximation to the nearest
hundredth.
StrategyFirst, we will find the radius of the circular base of the
cylinder.
WHYTo use the formula for the volume of a cylinder, ,
we need to know , the radius of the base.
SolutionSince a radius is one-half of the diameter of the circular base,

. From the figure, we see that the height of the cylinder is 10 cm.
To find the volume of the cylinder, we proceed as follows.
This is the formula for the volume of a cylinder.
Substitute 3 for r,the radius of the base,
and 10 for h,the height.
Evaluate the exponential expression: (3)^2 9.
Multiply: (9)(10) 90. Write the product so
that Pis the last factor.
Use a calculator to do the multiplication.
The exact volume of the cylinder is 90pcm^3. To the nearest hundredth, the volume
is 282.74 cm^3.

282.7433388

 90 p

Vp(9)(10)

Vp( 3 )^2 ( 10 )

Vpr^2 h

r^12 6 cm3 cm

r

Vpr^2 h

Self Check 5

Find the volume of the cylinder

shown below. Give the exact

answer and an approximation

to the nearest hundredth.

Now TryProblem 45

4 yd

10 yd

6 cm

10 cm

EXAMPLE (^6) Find the volume of the cone shown on
the right. Give the exact answer and an approximation to the
nearest hundredth.
StrategyWe will substitute 4 for and 6 for in the formula
and evaluate the right side.
WHYThe variable Vrepresents the volume of a cone.
V^13 pr^2 h
r h
4 ft
6 ft
1
1
2
 9
108