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The solid formed by revolving the graph of $f(x)=\cfrac{1}{x}$ over the domain $1\leq x$ about the $x$-axis is known as Torricelli's Trumpet (also known as Gabriel's Horn).

Find the volume, if it exists, for this solid.

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A

$\pi$

B

$\cfrac{\pi}{3}$

C

$1$

D

$\infty$

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