Question

The volume of a cylinder is given by the formula v= m'h. where r is the radius of the cylinder and h is the height.

Which expression represents the volume of this cylinder?
O
2x- 12rx?- 24 rX+ 63r
O
2x-5rx?-24 rX + 63 r
Oo 3 2 4O oo
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Answer 1

The Volume of cylinder is:
`\mathbf{Volume=2\pi x^3-5\pi x^2-24\pi x+63\pi }`

Option B is correct option.

Explanation:

We are given:

Volume of cylinder = h = 2x+7

Radius of cylinder = r = x-3

We need to find volume of cylinder

The formula used is:
`Volume=\pi r^2h`

Putting values and finding volume

`Volume=\pi r^2h\\Volume=\pi (x-3)^2(2x+7)\\Volume=\pi (x^2-6x+9)(2x+7)\\Volume=\pi (2x(x^2-6x+9)+7(x^2-6x+9))\\Volume=\pi (2x^3-12x^2+18x+7x^2-42x+63)\\Volume=\pi (2x^3-12x^2+7x^2-42x+18x+63)\\Volume=\pi (2x^3-5x^2-24x+63)\\Volume=2\pi x^3-5\pi x^2-24\pi x+63\pi \\`

So, The Volume of cylinder is:
`\mathbf{Volume=2\pi x^3-5\pi x^2-24\pi x+63\pi }`

Option B is correct option.