Chapter 12, Problem 16SGR

To determine

To find the lateral surface area and surface area of the given cylinder.

Answer to Problem 16SGR

  $40\pi$ inches², $72\pi$ inches²

Explanation of Solution

Given:

  

Radius of cylinder, $r=4$ inches.

Height of cylinder, $h=5$ inches.

Formula used:

Lateral surface area of a cylinder $=2\pi rh$

Surface area of a rectangular prism $=2\pi r\left(r+h\right)$

Calculation:

For the given cylinder,

Lateral surface area $=2\pi rh$

  $\begin{array}{l}=2\times \pi \times 4\times 5\\ =2\times \pi \times 20\\ =40\pi \end{array}$

Surface area $=2\pi r\left(r+h\right)$

  $\begin{array}{l}=2\times \pi \times 4\left(4+5\right)\\ =8\pi \left(9\right)\\ =72\pi \end{array}$

Conclusion:

Therefore, lateral surface area of the given cylinder is $40\pi$ inches² and surface area is $72\pi$ inches².