Question

A cylinder has a radius of 4x+2 and a height of 5x+4. Which polynomial in standard form best describes the total volume of the cylinder. Use the formula V=pir^2h for the volume of a cylinder.

Answer 1

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=4x+2\\ h=5x+4 \end{cases}\implies V=\pi (4x+2)^2(5x+4) \\\\\\ V=\pi [(4x+2)(4x+2)](5x+4)\\\\\\ V=\pi \stackrel{FOIL}{(16x^2+16x+4)}(5x+4) \\\\\\ V=\pi[ (80x^3+80x^2+20x)+(64x^2+64x+16)] \\\\\\ V=80\pi x^3+144\pi x^2+84\pi x+16\pi$