Barrons AP Calculus

Figure  N7–9

Example 5 __

A solid has as its base the circle x^2 + y^2 = 9, and all cross sections parallel to the
x-axis are squares. Find the volume of the solid.

SOLUTION:

Figure  N7–10

In Figure N7–10 the element of volume is a square prism with sides of length 2y
and thickness Δx, so .

Now, using symmetry across the y-axis, we find the volume of the solid: