Question

The volume of a cylinder is given by the formula V= pi^2h, where r is the radius of the cylinder and h is the height: which expression represents the volume of this cylinder?

Answer 1

Option B:
`(2\pi x^3 - 5\pi x^2 - 24\pi x + 63\pi )`

Explanation:

We know that height of the cylinder is given by h = 2x + 7 and radius r = x - 3.

We know that the formula of volume of a cylinder is:

Volume of a cylinder =
`\pi r^2 h`

Substituting the given values in the above formula to get:

Volume =
`\pi (x - 3)^2 *  (2x + 7)`

=
`\pi* (2x + 7)(x^2 - 6x + 9)`

=
`\pi *  (2x^3 - 12x^2 + 18x + 7x^2 - 42x + 63)`

=
`(2\pi x^3 - 5\pi x^2 - 24\pi x + 63\pi )`

Answer 2

ANSWER

B.

`V= {2\pi \: x}^(3) - 5\pi {x}^(2) - 24 \pi x + 63\pi`

EXPLANATION

The volume of the cylinder is given by:


`V=\pi r^2h`

From the diagram, the radius is


`r = x - 3`

and the height is


`h = 2x + 7`

We substitute into the formula to get,


`V= \pi(x - 3)^2(2x + 7)`

We expand to get,


`V= \pi( {x}^(2) - 6x + 9)(2x + 7)`


`V= \pi( {2x}^(3) - 12 {x}^(2) + 18x + 7 {x}^(2) - 42x + 63)`

This simplifies to,


`V= \pi( {2x}^(3) - 5 {x}^(2) - 24x + 63)`

We expand the bracket with the π to get,


`V= {2\pi \: x}^(3) - 5\pi {x}^(2) - 24 \pi x + 63\pi`