Question

A cone and a pyramid have the same height and same volume. If the radius of the base of the cone is r, what is the side length of the square base of the pyramid?

Answer 1

let Vc : cone's volume, Vp : pyramid's Volume, r radius, h height. w width and l length.


Vc=πr²h/3


Vp=(lwh)/3

make it equal to each other and cancel out the 3.

πr²h = lwh

heights will cancel out

πr²=lw

l=(πr²)/w