Chapter SH, Problem 12.6.6EP

To determine

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

Answer to Problem 12.6.6EP

The lateral area and surface area are respectively $\text{46}\text{.1}{\text{in}}^2,68.3{\text{in}}^2$ .

Explanation of Solution

Given:

Radius of the cylinder is 1.88 in.

Height is 3.9 in.

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 = 3.9 and radius is $r=1.88$ .

Lateral area is

  $\begin{array}{c}L=2\pi rh\\ =2\times \pi \times \left(1.88\right)\times 3.9\\ =14.664\pi \\ \approx 46.1\end{array}$

Surface area is

  $\begin{array}{c}S=L+2\pi r^2\\ =14.664\pi +2\times \pi \times {\left(1.88\right)}^2\\ =14.664\pi +7.0688\pi \\ =21.7328\pi \approx 68.3\end{array}$

Conclusion:

Hence, the lateral area and surface area are respectively $\text{46}\text{.1}{\text{in}}^2,68.3{\text{in}}^2$ .