Question

Find the volume v of the described solid s. the base of s is a circular disk with radius 5r. parallel cross-sections perpendicular to the base are squares.

Answer 1

(parallel cross-sections: "parallel" is a mistake)

The solid with circular bases, and square cross-sections perpendicular to the bases is a cylinder, whose height is equal to the diameter of a base circle.

Check the picture attached.

The radius is 5r, so the height=diameter=10r

Volume(cone)=S(base)*height=$\pi R^{2}*h= \pi (5r)^{2}*10r= \pi *25 *r^{2}*10r=250r ^{3}$ (units cube)


Answer: $250r ^{3}$