Question

The base of S is a circular disk with radius 4r. Parallel cross sections perpendicular to the base are squares. Find volume.

Answer 1

V = integral from -r to r of 4 ( r^2 - x^2 ) dx = ( 16/3) r^3

Here's the details:

eq of circle x^2 +y^2 = r^2 ==> y = sqrt( r^2 -x^2)

dV = ( 2y)^2 dx = 4y^2 dx = 4 (r^2 -x^2 ) dx