Question

A volleyball of radius 13 inches fits exactly in a cylinder with the same radius.

A sphere with a radius of 13 inches is inside of a cylinder with a radius of 13 inches. The cylinder has a height of 26 inches.

Inside the container there is empty space not taken up by the volleyball. What is the volume of that empty space? Use 3.14 for π and round the answer to the nearest cubic inch.

3,067 in.3
4,599 in.3
13,797 in.3
22,995 in.3

Answer 1

Cylinder volume = πr^2h = π(13^2)(26) = π(169)(26) = 4394π.

Sphere volume = (4/3)πr^3 = (4/3)π(13^3) = (4/3)π(2197) = (8788/3)π.

Empty space = cylinder − sphere = 4394π − (8788/3)π = (4394/3)π.

Using π = 3.14: (4394/3)·3.14 ≈ 4599.05 → 4599 in.^3.

Answer: 4,599 in.^3.