Chapter 12, Problem 12MCQ

To determine

To find the surface area of the given cone.

Answer to Problem 12MCQ

  $90\pi$ feet²

Explanation of Solution

Given:

  

Height of cone, $h=12$ feet

Radius of the base of cone, $r=5$ feet

Formula used:

Surface area of a cone $=\pi r\left(r+l\right)$

where $l=$ slant height of the cone.

Slant height $,l^2={\left(h\right)}^2+{\left(r\right)}^2\text{or}l=\sqrt{{\left(h\right)}^2+{\left(r\right)}^2}$

Calculation:

Since height of the cone is $h=12$ and radius of the base is $r=5$ ,

Therefore, slant height of the cone is given as

  $\Rightarrow {\left(12\right)}^2+{\left(5\right)}^2=l^2$

  $\begin{array}{l}\Rightarrow 144+25=l^2\\ \Rightarrow 169=l^2\\ \Rightarrow l=\sqrt{169}\\ \Rightarrow l=13\end{array}$

For the given cone,

Surface area $=\pi r\left(r+l\right)$

  $\begin{array}{l}=\pi \times 5\left(5+13\right)\\ =5\pi \left(18\right)\\ =90\pi \end{array}$

Conclusion:

Therefore, surface area of the given cone is $90\pi$ feet².