MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A solid has base the circular disk x2+y2≤9. For every x-value in the base, the cross section perpendicular to the x-axis is a square.
(a) Express the side length of an arbitrary square cross section as a function of x.
(b) Write—but do not yet evaluate—the definite integral that represents the volume of the solid.
(c) Evaluate the integral from part (b) to obtain the exact volume.