Question

A hollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. Find the volume of the foam.

Answer 1

Answer:

                             π

V-foam = 4r³( 2 - ----- )

                             3

Step-by-step explanation:

Let the radius of the sphere be r.  Then the volume of the sphere is

V = (4/3)(π)(r³).  

Next, recognize that the side length of the cube is 2r, and that the volume of the cube is thus

V = (2r)³, or 8r³.

Then the volume of the foam is equal to the volume of the cube less the volume of the sphere:

V-foam = 8r³ - (4/3)(π)(r³).  This could be factored into

                             π

V-foam = 4r³( 2 - ----- )

                             3