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You are given the region bounded by the lines $f(x)=x$, $g(x)=4x$, and $x=2$.

Find the volume of the solid formed when this region is revolved about the $x$-axis.

A

$\dfrac { 8\pi }{ 3 }$

B

$10\pi $

C

$20\pi $

D

$40\pi $

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