Chapter 12.8, Problem 33SR

To determine

To find: the lateral and surface area

Answer to Problem 33SR

The lateral area of the cylinder is $200.96i{n}^2$ .

The surface area of the cylinder is $602.88i{n}^2$ .

Explanation of Solution

Given:

  

Formula used:

The lateral area $L$ of a cylinder is calculated as

  $L=2\pi rh$

The surface area $S$ of a rectangular prism is calculated as

  $S=L+2B$

Calculation:

Consider the diameter of the cylinder is $16in.$ and the height of the cylinder is $4in.$

The objective is to find the lateral and surface area of the cylinder.

Now, find the lateral area of the cylinder.

Since radius is half the diameter of a circle, so radius is $\frac{16}{2}in.$ that is

  $8in.$

Put $r=8$ and $h=4$ in the lateral area formula to find the lateral area of the cylinder.

Thus,

  $\begin{array}{l}L=2\pi rh\\ =2\pi \left(8\right)4\\ =2\pi \left(32\right)\\ =64\pi \\ \approx 64\left(3.14\right)[Since\pi \approx 3.14]\\ =200.96\end{array}$

Therefore, the lateral area of the cylinder is approximately $200.96i{n}^2$ .

Next find the surface area of the cylinder.

First find the area $B$ of the circular base of the cylinder. The area $B$ of the base is given by

  $B=\pi r^2$ Where $r$ is the radius of the circle.

  $\begin{array}{l}=\pi {\left(8\right)}^2\\ =64\pi \\ \approx 64(3.14)[\pi \approx 3.14]\\ =200.96\end{array}$

Put $B\approx 200.96$ and $L\approx 200.96$ in the surface area formula to find the surface area of the cylinder.

  $\begin{array}{l}S=L+2B\\ \approx 200.96+2\left(200.96\right)\\ =200.96+401.92\\ =602.88\end{array}$

Therefore, the surface area of the cylinder is approximately $602.88i{n}^2$ .

Conclusion:

Therefore, the lateral area of the cylinder is $200.96i{n}^2$ and the surface area of the cylinder is $602.88i{n}^2$ .