Chapter SH, Problem 12.6.8EP

To determine

To find: the lateral area and surface area of a cylinder.

Answer to Problem 12.6.8EP

The lateral area and surface area are respectively $53{\text{yd}}^2,84.8{\text{yd}}^2$ .

Explanation of Solution

Given:

Diameter of the cylinder is 4.5 yd.

Height is 3.75 yd.

Formula used:

Lateral area of the cylinder is $L=2\pi rh$

Total surface area of the cylinder is $S=L+2\pi r^2$

Calculation:

Lateral area of the cylinder is

  $L=2\pi rh$

Total surface area of the cylinder is

  $S=2\pi rh+2\pi r^2\to S=L+2\pi r^2$

Height is h = 3.75 and radius is $r=\frac{4.5}{2}\to r=2.25$ .

Lateral area is

  $\begin{array}{c}L=2\pi rh\\ =2\times \pi \times 2.25\times 3.75\\ =16.875\pi \\ \approx 53\end{array}$

Surface area is

  $\begin{array}{c}S=L+2\pi r^2\\ =16.875\pi +2\times \pi \times {\left(2.25\right)}^2\\ =163.875\pi +10.125\pi \\ =27\pi \approx 84.8\end{array}$

Conclusion:

Hence, the lateral area and surface area are respectively $53{\text{yd}}^2,84.8{\text{yd}}^2$ .