Step 1

Find the volume of the resulting solid.

Step 2

Let the volume of the circular cylinder be \(V_{1}\ \text{and let the volume of the right circular cone be}\ V_{2}.\)

A solid formed by cutting a conical section away from a right circular cylinder.

Find the volume \(V_{1}.\)

\(\displaystyle{V}_{{1}}=\pi{r}^{2}{h}\)

\(\displaystyle=\pi{\left({6}\right)}^{2}{\left({8}\right)}\)

\(= 288\ \pi\)

Find the volume \(V_{2}.\)

\(\displaystyle{V}_{{2}}=\frac{1}{{3}}\pi{r}^{2}{h}\)

\(\displaystyle=\frac{1}{{3}}\pi{\left({6}^{2}{\left({8}\right)}\right.})\)

\(= 96\ \pi\)

Step 3

Find the volume of the resulting solid.

\(\displaystyle{V}={V}_{{1}}-{V}_{{2}}\)

\(\displaystyle={288}\pi-{96}\pi\)

\(= 192\ \pi\)

\(\displaystyle\approx{603}.{19}\in^{2}\)

Hence, the volume of the resulting solid \(\displaystyle{603.19}\in^{2}\)