Chapter 12.7, Problem 32SR

To determine

To find: the lateral and surface area

Answer to Problem 32SR

The surface area of the cylinder is approximately $92.17m^2$ .

The lateral area of the cylinder is approximately $41.17m^2$ .

Explanation of Solution

Given:

Cylinder diameter 5.7 meters, height 2.3 meters

Formula used:

The lateral area L of a cylinder is $L=2\pi rh$ .

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

The surface area S of a rectangular prism is S = L + 2B.

Here, L is the lateral area and B is the area of the base.

Calculation:

Consider the diameter of the cylinder is 5.7 m and the height of the cylinder is 2.3 m.

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

Find the lateral area of the cylinder as follows:

Since radius is half the diameter of a circle.

Therefore, the radius of the circle is,

  $\begin{array}{l}r=\frac{5.7}{2}m\\ =2.85m\end{array}$

Substitute $r=2.85$ and $h=2.3$ in $L=2\pi rh$

  $\begin{array}{l}L=2\pi rh\\ =2\pi \left(2.85\right)\left(2.3\right)\\ =2\pi \left(6.555\right)\\ =13.11\pi \\ \approx 13.11\left(3.14\right)\\ \approx 41.17\end{array}$

Hence, the lateral area of the cylinder is approximately $41.17m^2$ .

Find the surface area of the cylinder as follows:

The area B of the base is $B=\pi r^2$ .

Here, r is the radius of the circle.

Substitute $r=2.85$ in $B=\pi r^2$

  $\begin{array}{l}B=\pi {\left(2.85\right)}^2\\ =8.1225\pi \\ \approx 8.1225\left(3.14\right)\\ \approx 25.5\end{array}$

Substitute $B\approx 25.5$ and $L\approx 41.17$ in $S=L+2B$

  $\begin{array}{l}S=L+2B\\ \approx 41.17+2\left(25.5\right)\\ =41.17+51\\ =92.17\end{array}$

Hence, the surface area of the cylinder is approximately $92.17m^2$ .

Conclusion:

Hence, the surface area of the cylinder is approximately $92.17m^2$ andthe lateral area of the cylinder is approximately $41.17m^2$ .