Chapter 12, Problem 17SGR

To determine

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

Answer to Problem 17SGR

Lateral surface $=113$ square centimeters

Surface area $=170$ square centimeters

Explanation of Solution

Given:

  

A cylinder

Radius, $(r)=3$ centimeters

Height, $(h)=6$ centimeters

Formula used:

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

where $r$ is the radius and $h$ is the height of the cylinder.

Total surface area of cylinder $=2\pi r(h+r)$

where $r$ is the radius and $h$ is the height of the cylinder.

Calculation:

To find the lateral surface area of the cylinder, use the following formula.

Lateral surface area $=2\pi rh$

Now putting the values,

  $\Rightarrow 2\times 3.14\times 3\times 6$

  $\Rightarrow 113.04$ square centimeters

So, the lateral surface area of the cylinder is 113 square centimeters.

To find the surface area of the cylinder, use the following formula.

Lateral surface area $=2\pi r(h+r)$

Now putting the values,

  $\Rightarrow 2\times 3.14\times 3\times (6+3)$

  $\Rightarrow 2\times 3.14\times 3\times 9$

  $\Rightarrow 169.56$ square centimeters

So, the lateral surface area of the cylinder is 170 square centimeters.

Conclusion:

Hence, the lateral surface area is 113 square centimeters and surface area is 170 square centimeters.