Chapter 11.10, Problem 7P

To determine

To find: The volume of the cylinder in terms of $\pi$ .

Answer to Problem 7P

The volume is $V=8100\pi {\text{cm}}^3$ .

Explanation of Solution

Given:

The radius of the cylinder is $r=15\text{cm}$ .

The height of the cylinder is $h=36\text{cm}$ .

The radius of the cylinder is $r=\sqrt{\frac{V}{\pi h}}$

Calculation:

Consider the radius of the cylinder is of the form,

  $r=\sqrt{\frac{V}{\pi h}}$

Then, the volume is calculated as.,

  $\begin{array}{l}15\text{cm}=\sqrt{\frac{V}{\pi \left(36\text{cm}\right)}}\\ \frac{V}{\pi \left(36\text{cm}\right)}=225{\text{cm}}^2\\ V=225{\text{cm}}^2\left(\pi \left(36\text{cm}\right)\right)\\ V=8100\pi {\text{cm}}^3\end{array}$