Question

A sphere with a diameter of 9 units fits exactly in the clear glass cube as shown.

A sphere is inside of a cube. The cube has side lengths of 9 units.

Which expression represents the volume, in cubic units, of empty space in the cube?

Four-thirdsπ(4.53) – (4.5)3
(9)3 – Four-thirdsπ(4.52)
Four-thirdsπ(4.53) – (9)3
(9)3 – Four-thirdsπ(4.53)

Answer 1

Empty space = cube volume − sphere volume. Cube volume = 9^3. Sphere volume = (4/3)π(4.5)^3 (radius = 9/2 = 4.5).

So the correct expression is: (9)^3 − (4/3)π(4.5)^3. (The last choice.)