Chapter 12, Problem 12PT

To determine

To calculate:To find the lateral and surface area of solid and round to the nearest tenth, if necessary

Answer to Problem 12PT

The lateral surface area of cone is $47.1m^3$ and total surface area of cone is $75.4m^3$

Explanation of Solution

Given information:Solid is

  

Formula Used:

Lateral surface area of prism is calculated as

  $LSA=\pi r\sqrt{h^2+r^2}$

Where,

  $r=$ Radius

  $h=$ Height

Total surface area of prism is calculated as

  $SA=\pi r\sqrt{h^2+r^2}+\pi r^2$

Calculation:

Solid is given as

  

Lateral surface area of cone is calculated as

  $LSA=\pi r\sqrt{h^2+r^2}$

Substituting the values

  $\begin{array}{l}LSA=\frac{22}{7}\times 3\sqrt{4^2+3^2}\\ LSA=\frac{22}{7}\times 3\sqrt{16+9}\\ LSA=\frac{22}{7}\times 3\sqrt{25}\\ LSA=\frac{66}{7}\times 5\\ LSA=\frac{330}{7}\\ LSA\approx 47.1m^3\end{array}$

Total surface area of prim is calculated as

  $LSA=\pi r\sqrt{h^2+r^2}+\pi r^2$

Substituting the values

  $\begin{array}{l}SA=47.1+\left(\frac{22}{7}\times 3\times 3\right)\\ SA=47.1+\left(\frac{198}{7}\right)\\ SA=47.1+28.28\\ SA=75.38\\ SA=75.4m^3\end{array}$

Conclusion:

Hence,lateral surface area is $47.1m^3$ total surface area is $75.4m^3$