A souvenir consisting of a cube with an inserted sphere is made to represent Earth. Both pieces are made out of solid crystal. The sphere replaces one quarter of the volume of the cube. Calculate the volume of the souvenir piece.

Question

The sphere has diameter of 4 cm and the cube had side length of 4cm.

I know to use formulas for volume for both shapes but after that I am completely lost. Please Help!!!
Thank you.

Answer 1

cube has volume 4^3 = 64
sphere has volume π/6 * 4^3 = 64π/6

Now just subtract the volumes:

64(1 - π/6)

Actually, the wording is a bit vague. Since the sphere has replaced some of the cube, the space is still occupied, so the whole cube constitutes the souvenir. volume=64 cm^3

Answer 2

81.5