Question

Find the volume of the solid whose base is the circle x^2+y^2=64 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.

Answer 1

1) x² + y² = 64 is the EQUAION of a cercle with a radius R = √64 =8

2) The cross section is a triangle with H = BASE.
Since R = 8 that means the Base B= 16 and also the height H =16
This  solid is then a regular cone and its Volume value is
V = πR².H
V π(8)².(16) = 2014π units³ or ≈ 3217 units³