A sphere with a diameter of 24 inches is reshaped into a cone with a radius of 32 inches. If all the material is used, what is the height of the cone?

Answer 1

sphere: radius = s
cone: radius c, height h

4π/3 s^3 = π/3 c^2 h
4s^3 = c^2 h
4(12^3) = (32^2)h
h = 4*4^3*3^3/2^10 = 3^3/2^2 = 27/4 = 6.75