# A solid is formed by cutting a conical section away a right circular cylinder. If the radius measures 6 in. and the altitude measures 8 in., what is the volume of the resulting solid?

A solid is formed by cutting a conical section away a right circular cylinder. If the radius measures 6 in. and the altitude measures 8 in., what is the volume of the resulting solid?
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stuth1

Step 1
Find the volume of the resulting solid.
Step 2
Let the volume of the circular cylinder be
A solid formed by cutting a conical section away from a right circular cylinder.
Find the volume ${V}_{1}.$
${V}_{1}=\pi {r}^{2}h$
$=\pi {\left(6\right)}^{2}\left(8\right)$

Find the volume ${V}_{2}.$
${V}_{2}=\frac{1}{3}\pi {r}^{2}h$
$=\frac{1}{3}\pi \left({6}^{2}\left(8\right)\right)$

Step 3
Find the volume of the resulting solid.
$V={V}_{1}-{V}_{2}$
$=288\pi -96\pi$

$\approx 603.19{\in }^{2}$
Hence, the volume of the resulting solid $603.19{\in }^{2}$

Jeffrey Jordon