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?

Answer 1

Answer: the answer is D or the equation in the attached photo :)

Answer 2

347.3 cubic units

Explanation:

To find the area of empty space, we can find the volume of both shapes and subtract the volume of the sphere from the volume of the cube.

Volume of a cube = l^3

Our given length in this case is 9, so the volume is 9x9x9= 729 cubic units.

The volume of sphere = 4/3 pi r^3

Our radius is 4.5 (half of diameter), so:

4/3*91.125 pi

121.5 pi = 381.7 (1dp)

729-381.7 = 347.3

The volume of empty space = 347.3 cubic units.

The full expression in terms of given d:

Volume of empty space = d^3 - 4/3 pi (d/2)^3

Hope this helped!