what is the volume of a sphere that has the same diameter and height of a cylinder that is 24 cubic feet in volume?

So you are saying the diameter is equal to the height of the cyliner ?

let the radius be r
then the height is 2r
volume of cylinder = πr^2h
= πr^2(2r) = 2πr^3
2πr^3 = 24
πr^3 = 12

but volume of sphere = (4/3)πr^3
= (4/3)(12) = 16