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

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,

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

Answer 2

Answer:

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

Step-by-step 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 = $\pi (x - 3)^2 * (2x + 7)$

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

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

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