Chapter SH, Problem 12.6.5EP

To determine

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

Answer to Problem 12.6.5EP

The lateral area and surface area are respectively $\text{78}\text{.5}{\text{cm}}^2,117.8{\text{cm}}^2$ .

Explanation of Solution

Given:

Diameter of the cylinder is 5cm.

Height is 5cm.

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 = 5 and radius is $r=\frac{5}{2}\to r=2.5$ .

Lateral area is

  $\begin{array}{c}L=2\pi rh\\ =2\times \pi \times 2.5\times 5\\ =25\pi \\ \approx 78.5\end{array}$

Surface area is

  $\begin{array}{c}S=L+2\pi r^2\\ =25\pi +2\times \pi \times {\left(2.5\right)}^2\\ =25\pi +12.5\pi \\ =37.5\pi \approx 117.8\end{array}$

Conclusion:

Hence, the lateral area and surface area are respectively $\text{78}\text{.5}{\text{cm}}^2,117.8{\text{cm}}^2$ .