Question

The volume of a cylinder is given by the formula V= πr^2h, where r is the radius of the cylinder and h is the height. Suppose a cylindrical can has radius (x + 8) and height (2x + 3). Which expression represents the volume of the can?

Answer 1

The volume of the cylinder is defined by the expression
`V=\pi (x+8)^2(2x+3)\text{ or }V=\pi (2 x^3 + 35 x^2 + 176 x + 192)`.

Explanation:

The volume of a cylinder is given by the formula

`V=\pi r^2h`

Where, r is the radius of the cylinder and h is the height.

The radius of the cylinder is (x+8) and the height of the cylinder is (2x+3).

Substitute r = (x+8) and h = (2x+3) in the given formula.

`V=\pi (x+8)^2(2x+3)`

`V=\pi (x^2+16x+64)(2x+3)`
`[\because (a+b)^2=a^2+2ab+b^2]`

`V=\pi (2 x^3 + 35 x^2 + 176 x + 192)`

Therefore volume of the cylinder is defined by the expression
`V=\pi (x+8)^2(2x+3)\text{ or }V=\pi (2 x^3 + 35 x^2 + 176 x + 192)`.

Answer 2

we know that

The volume of a cylinder is given by the formula

`V=\pi r^(2) h`

where

r is the radius of the cylinder

h is the height of the cylinder

in this problem

`r=x+8\\ h=2x+3`

Substitute the values in the formula above

`V=\pi*(x+8)^(2)*(2x+3)`

`V=\pi*(x^(2)+16x+64)*(2x+3) \\ V=\pi *(2x^(3) +3x^(2) +32x^(2) +48x+128x+192)\\ V=\pi *(2x^(3) +35x^(2) +176x+192)`

therefore

the answer is

The volume of the can is equal to

`V=\pi *(2x^(3) +35x^(2) +176x+192) units ^(3)`