Question

The diameter and height of this cylinder are equal to the side length, S, of the cube in which the cylinder is inscribed. What is the expression for the cylinder's volume?

Answer 1

Find the radius

Radius = Diameter ÷ 2

Radius of the cylinder = S ÷ 2 = S/2

Find the height:

Height of the cylinder = S (Given)

Find the volume:

Volume of a cylinder = πr²h

Volume of the cylinder = π(S/2)²(S) = (S³/4)π

Answer: The volume of the cylinder = (S³/4)π units³