A sphere with a diameter of 30 inches is placed in a cube. The sphere touches the lateral faces

and the bases of the cube. Find:

a. The dimensions of the cube.

b. The volume of the cube.

c. The volume of the sphere.

d. The volume inside the cube that is not taken up by the sphere.

a) 30 inches * 30 inches * 30 inches

b) 27,000 inches³

c) 14,130 inches³

d) 12,870 inches³

Step-by-step explanation:

Edge of the cube = diameter = 30 inches

Volume of cube = s³

30³ = 27000 inches³

Radius = 30/2 = 15

Volume of sphere:

(4/3) * 3.15 * 15³

14130 inches³

Difference:

27000 - 14130

12870 inches³