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 c

ylinder. Use the formula V=pir^2h for the volume of a cylinder.

Mathematics

1 answer:

Viefleur [7K]4 years ago

6 0

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

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