Question

a sphere fits snugly inside a 6-in. cube as shown. what is the volume of the region inside the cube but outside the sphere

Answer 1

The six inch cube has a volume of 216 in³.
6*6*6=216
The sphere has a volume of 105.975 in³ (assuming pi is 3.14)
Because the sphere fits snugly inside the cube, it has a diameter of 6 inches and a radius of three inches.
4/3 π r³
4/3 π 3³
4/3 π  27
4/3(3.14)(27)
105.975

The volume of the region outside the sphere but inside the cube can be found by subtracting the area of the sphere from the area inside the cube.
216 - 105.975 = 110.025

The volume of the region outside of the sphere but inside the cube is 110.025 in ³