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

Answer:

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

Step-by-step 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

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