Chapter 12, Problem 36SGR

To determine

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

Answer to Problem 36SGR

Lateral surface area of cone is $264f{t}^2$ and total surface area of cone is $308f{t}^2$

Explanation of Solution

Given information:Cone is

  

Formula Used:

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

  

  $Lateralsurfaceare{a}_{Cone}=\pi rl$

  $Surfaceare{a}_{Cone}=\pi rl+\pi r^2$

Where,

  $r=$ Radius of base

  $l=$ slant height

Calculation:

Cone is given as follows

  

Here, dimensions of coneare as follows:

  $\begin{array}{l}r=7ft\\ l=12ft\end{array}$

Lateral surface of cone is calculated as follows:

  $Lateralsurfaceare{a}_{Cone}=\pi rl$

Substituting the values, volume is

  $\begin{array}{l}Lateralsurfaceare{a}_{Cone}=\frac{22}{7}\times 7\times 12\\ Lateralsurfaceare{a}_{Cone}=22\times 12\\ Lateralsurfaceare{a}_{Cone}=264f{t}^2\end{array}$

Surface area of coneis calculated as follows:

  $Surfaceare{a}_{Pyramid}=2\left(bs\right)+b^2$

Substituting the values, volume is

  $\begin{array}{l}Surfaceare{a}_{Cone}=\left(\frac{22}{7}\times 7\times 12\right)+\left(\frac{22}{7}\times 7\times 7\right)\\ Surfaceare{a}_{Cone}=\left(22\times 12\right)+\left(22\times 7\right)\\ Surfaceare{a}_{Cone}=264+154\\ Surfaceare{a}_{Cone}=308f{t}^2\end{array}$

Conclusion:

Hence, Lateral surface area of cone is $264f{t}^2$ and total surface area of cone is $308f{t}^2$