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

B.
[tex]V= {2\pi \: x}^{3} - 5\pi {x}^{2} - 24 \pi x + 63\pi [/tex]

EXPLANATION

The volume of the cylinder is given by:

[tex]V=\pi r^2h[/tex]

From the diagram, the radius is

[tex]r = x - 3[/tex]

and the height is

[tex]h = 2x + 7[/tex]

We substitute into the formula to get,

[tex]V= \pi(x - 3)^2(2x + 7)[/tex]

We expand to get,

[tex]V= \pi( {x}^{2} - 6x + 9)(2x + 7)[/tex]

[tex]V= \pi( {2x}^{3} - 12 {x}^{2} + 18x + 7 {x}^{2} - 42x + 63)[/tex]

This simplifies to,

[tex]V= \pi( {2x}^{3} - 5 {x}^{2} - 24x + 63)[/tex]

We expand the bracket with the π to get,

[tex]V= {2\pi \: x}^{3} - 5\pi {x}^{2} - 24 \pi x + 63\pi [/tex]

alinakincsem alinakincsem · Answer 2 · 2019-01-26T13:22:01+01:00

Answer:

Option B: [tex](2\pi x^3 - 5\pi x^2 - 24\pi x + 63\pi )[/tex]

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 = [tex] \pi r^2 h [/tex]

Substituting the given values in the above formula to get:

Volume = [tex]\pi (x - 3)^2 * (2x + 7)[/tex]

=[tex]\pi* (2x + 7)(x^2 - 6x + 9)[/tex]

= [tex]\pi * (2x^3 - 12x^2 + 18x + 7x^2 - 42x + 63)[/tex]

= [tex](2\pi x^3 - 5\pi x^2 - 24\pi x + 63\pi )[/tex]