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

(1024/3)r^3.

Step-by-step explanation:

Step one: So, we have that x^2 + y^2 = 4^2 × r^2(when z component = 0) . Hence, there is the need to make y^2 the subject of the formula.

Step two: 4y^2 = 16r^2 - x^2. Where 4 ×(16r^2 - x^2) is the the cross sectional area.

Step three: the next thing to do here is to integrate the cross sectional area making 4r and -4r the upper limit and lower limit for the integration.

Step four: the integration will then give a product (16 × 64)/3 A = (1024/3)r^3.