Chapter 12, Problem 37SGR

To determine

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

Answer to Problem 37SGR

Lateral surface area of cone is $132i{n}^2$ and total surface area of cone is $182.3i{n}^2$

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:

  $\begin{array}{l}r=4in.\\ l=10.5in\end{array}$

Lateral surface of cone is calculated as follows:

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

Substituting the values, volume is

  $\begin{array}{l}Lateralsurfaceare{a}_{Cone}=\frac{22}{7}\times 4\times 10.5\\ Lateralsurfaceare{a}_{Cone}=22\times 4\times 1.5\\ Lateralsurfaceare{a}_{Cone}=132i{n}^2\end{array}$

Surface area of coneis calculated as follows:

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

Substituting the values, volume is

  $\begin{array}{l}Surfaceare{a}_{Cone}=\left(\frac{22}{7}\times 4\times 10.5\right)+\left(\frac{22}{7}\times 4\times 4\right)\\ Surfaceare{a}_{Cone}=\left(22\times 4\times 1.5\right)+50.28\\ Surfaceare{a}_{Cone}=132+50.28\\ Surfaceare{a}_{Cone}=182.28\\ Surfaceare{a}_{Cone}=182.3i{n}^2\end{array}$

Conclusion:

Hence, Lateral surface area of cone is $132i{n}^2$ and total surface area of cone is $182.3i{n}^2$