Question

the volume of a cylinder can be found using the formula $v = \pi r^{2}h$ where $r$ is the radius of the base and $h$ is the height. which expression could represent the volume of the given cylinder if the radius is $(x + 3)$ and the height is $(2x)$?

Explanation:

Step1: Substitute r and h into formula

$V = \pi (x+3)^2 (2x)$

Step2: Expand $(x+3)^2$

$(x+3)^2 = x^2 + 6x + 9$

Step3: Multiply by $2x$ and $\pi$

$V = \pi \cdot 2x(x^2 + 6x + 9) = \pi(2x^3 + 12x^2 + 18x)$

Answer:

$\pi(2x^3 + 12x^2 + 18x)$ or $2\pi x^3 + 12\pi x^2 + 18\pi x$