Chapter 12.4, Problem 18PPS

To determine

To find:

The volume of the cylinder.

Answer to Problem 18PPS

The volume of the cylinder is $\text{823}{\text{.3 in}}^3$ .

Explanation of Solution

Given information:

  

Calculation:

Apply the Pythagorean theorem to find the height of the cylinder.

Assume that the height of the cylinder is $h\text{ in}$ .

  $a^2+b^2=c^2$

Substitute $a=h$ , $b=11$ and $c=14$ in the above formula:

  $\begin{array}{c}{a}^2+b^2=c^2\\ h^2+{11}^2={14}^2\\ h^2={14}^2-{11}^2\\ h^2=196-121\\ h^2=75\\ h=\sqrt{75}\\ =8.66\end{array}$

Diameter of the cylinder is $11\text{ in}$ .

So, the radius of the cylinder is $\frac{11}{2}=5.5\text{ in}$ .

Volume of the cylinder is:

  $V=\pi r^{2}h$

Substitute $r=5.5$ and $h=8.66$ in the above formula:

  $\begin{array}{c}V=\pi {\left(5.5\right)}^{2}8.66\\ =\pi \left(30.25\right)8.66\\ =261.965\pi \\ \approx 823.3{\text{ in}}^3\end{array}$

Hence the volume of the cylinder is $\text{823}{\text{.3 in}}^3$ .