278 STEP 4. Review the Knowledge You Need to Score High
Example 2
Find the volume of a pyramid whose base is a square with a side of 6 feet long and a height
of 10 feet. (See Figure 12.4-3.)
x
y
0
10
6
6
s
x
3
10
Figure 12.4-3
Step 1. Find the area of a cross sectionA(x). Note each cross section is a square of side 2s.
Similar triangles:
x
s
=
10
3
⇒s=
3 x
10
.
A(x)=(2s)^2 = 4 s^2 = 4
(
3 x
10
) 2
=
9 x^2
25
Step 2. Set up an integral.
V=
∫ 10
0
9 x^2
25
dx
Step 3. Evaluate the integral.
V=
∫ 10
0
9 x^2
25
dx=
3 x^3
25
] 10
0
=
3 ( 10 )^3
25
− 0 = 120
The volume of the pyramid is 120 ft^3.