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iogann1982 [59]
3 years ago
11

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 expr

ession represents the volume of this cylinder?

Mathematics
2 answers:
Neporo4naja [7]3 years ago
4 0
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
kicyunya [14]3 years ago
4 0

<u>Answer:</u>

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

<u>Step-by-step explanation:</u>

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:

<em>Volume of a cylinder = \pi r^2 h</em>

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 )

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