Mathematics: 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?

The volume of a cylinder is given by the formula

Ответ:

bayloann2621

09.03.2022

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,

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