Chapter 12, Problem 19CUR

To determine

To find: The volume of cylinder if radius is equal to its height.

Answer to Problem 19CUR

Thevolumeof the cylinder is $125\pi {\text{cm}}^3$ .

Explanation of Solution

Given information:The cylinder has a radius equal to its height and the total area is $100\pi {\text{cm}}^2$ .

Calculation:

The formula to find the totalarea $\left(TA\right)$ of the cylinder is:

  $TA=2\pi r\left(h+r\right)$

Here, $r$ is the radius and $h$ is the height of cylinder.

It is given that the radius of cylinder and height is equal. So,

  $r=h$

Substitute $r$ for $h$ and $100{\text{cm}}^2$ for $TA$ in the above formula.

  $\begin{array}{c}100\pi =2\pi r\left(r+r\right)\\ \frac{100\pi }{2\pi }=2r^2\\ 25=r^2\\ r=5\text{cm}\end{array}$

The volume of cylinder can be calculated as:

  $\begin{array}{c}V=\pi r^{2}h\\ =\pi r^3\\ =\pi \times {\left(5\right)}^3\\ =125\pi {\text{cm}}^3\end{array}$

Therefore, the volume of the cylinder is $125\pi {\text{cm}}^3$ .