Chapter SH, Problem 12.6.3EP

To determine

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

Answer to Problem 12.6.3EP

The lateral area and surface area are respectively $\text{263}\text{.9}{\text{cm}}^2,374.7{\text{cm}}^2$ .

Explanation of Solution

Given:

Area:

Radius of the cylinder is 4.2 m.

Height is 10 m.

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 = 10 and radius is $r=4.2$ .

Lateral area is

  $\begin{array}{c}L=2\pi rh\\ =2\times \pi \times 4.2\times 10\\ =84\pi \\ \approx 263.9\end{array}$

Surface area is

  $\begin{array}{c}S=L+2\pi r^2\\ =84\pi +2\times \pi \times {\left(4.2\right)}^2\\ =84\pi +35.28\pi \\ =119.28\pi \approx 374.7\end{array}$

Conclusion:

Hence, the lateral area and surface area are respectively $\text{263}\text{.9}{\text{cm}}^2,374.7{\text{cm}}^2$ .