Question

The volume of a cylinder is given by the formula y = 72h, where r is the radius of the cylinder and h is the height.Which expression represents the volume of this cylinder?h = 2x+7r=x-3

Answer 1

Given the formula of the volume of the cilinder:

`V=\pi\cdot r^2\cdot h`

if we have that r = x - 3 and h = 2x + 7, then we get the following when applying the formula:

`\begin{gathered} h=2x+7 \\ r=x-3 \\ \Rightarrow V=\pi\cdot(x-3)^2(2x+7)_{} \end{gathered}`

When we simplify the product of binomials,we get the following:

`\begin{gathered} V=\pi\cdot(x-3)^2(2x+7) \\ =\pi\cdot(x^2-6x+9)\cdot(2x+7) \\ =\pi\cdot(2x^3+7x^2-12x^2-42x+18x+63) \\ =\pi\cdot(2x^3-5x^2-24x+63) \\ =2\pi x^3-5\pi x^2-24\pi x+63\pi \end{gathered}`

therefore, the volume of the cilinder is:

`V=2\pi x^3-5\pi x^2-24\pi x+63\pi`