Chapter 12.3, Problem 5BCYP

To determine

Find the surface area of the cone.

Answer to Problem 5BCYP

S = $286.9i{n}^2$

Explanation of Solution

Given:

  

Formula Used: The Lateral area L of cone is

  $L=\pi rl$ , where l is the slant height and r is the radius of the base.

The Surface area S of cone is

  $S=L+\pi r^2$ , where r is the radius of the base.

Calculation:

Radius of the cone is 6 in. and height is 7 in.

Find Slant height using the Pythagoras theorem:

l = $\sqrt{6^2+7^2}=\sqrt{36+49}=\sqrt{85}$

Lateral area of the cone = $L=\pi rl=\pi (6)(\sqrt{85})\approx 173.78i{n}^2$

Surface area of the cone = $S=L+\pi r^2=173.78+\pi {(6)}^2=173.78+113.09\approx 286.9i{n}^2$

Hence,

S = $286.9i{n}^2$