Chapter 12, Problem 32SGR

To determine

To calculate:To find the lateral and surface area of cylinder and round to the nearest tenth

Answer to Problem 32SGR

Lateral surface area of cylinder is $132m^2$ and total surface area of cylinder is $188.6m^2$

Explanation of Solution

Given information:Cylinder is

  

Formula Used:

Lateral and surface area of cylinder is given by the below formula:

  $Lateralsurfaceare{a}_{Cylinder}=2\pi rh$

  $Surfaceare{a}_{Cylinder}=2\pi rh+2\pi r^2$

Where,

  $r=$ Radius of base of cylinder

  $h=$ Height of cylinder

Calculation:

Cylinder is given as follows

  

Here, dimensions of cylinderas follows:

  $\begin{array}{l}r=3cm\\ h=7cm\end{array}$

Lateral surface of cylinder is calculated as follows:

  $Lateralsurfaceare{a}_{Cylinder}=2\pi rh$

Substituting the values, volume is

  $\begin{array}{l}Lateralsurfaceare{a}_{Cylinder}=2\times \frac{22}{7}\times 3\times 7\\ Lateralsurfaceare{a}_{Cylinder}=2\times 22\times 3\\ Lateralsurfaceare{a}_{Cylinder}=132m^2\end{array}$

Surface area of cylinder is calculated as follows:

  $Surfaceare{a}_{Cylinder}=2\pi rh+2\pi r^2$

Substituting the values, volume is

  $\begin{array}{l}Surfaceare{a}_{Cylinder}=\left(2\times \frac{22}{7}\times 3\times 7\right)+\left(2\times \frac{22}{7}\times 3\times 3\right)\\ Surfaceare{a}_{Cylinder}=132+56.57\\ Surfaceare{a}_{Cylinder}=188.57m^2\\ Surfaceare{a}_{Cylinder}=188.6m^2\end{array}$

Conclusion:

Hence, Lateral surface area of cylinder is $132m^2$ and total surface area of cylinder is $188.6m^2$