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

Volume of cylinder = pi r^2 h

diameter = S so the radius = 0.5S and the height of cylinder = S

so Volume of this cylinder = pi (0.5S)^2 * S

= 0.25 pi S^3

Answer 2

Expression for given volume =
`\pi (S^3)/(8)`

Explanation:

Length of cube is given to be S

therefore Height of the Cylinder = S

Diameter of the Cylinder = S

Radius of Cylinder =
`(S)/(2)`

Formula for the volume of Cylinder =
`\pi r^2 h`

where r = radius of cylinder

h = height of cylinder

Volume =
`\pi({(S)/(2))^(2) S`

=
`\pi (S^3)/(8)`