Chapter 12.3, Problem 6CYU

To determine

Find the lateral area of the conical tent.

Answer to Problem 6CYU

L = $395.1c{m}^2$

S = $571.8c{m}^2$

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:

Diameter of the cone is 15 cm and height is 15 cm.

radius = r = $\frac{15}{2}=7.5cm$ inches

Use Pythagoras Theorem to find the slant height of the cone = l = $\sqrt{{15}^2+{7.5}^2}\approx 16.77cm$

Lateral area of the cone = $L=\pi rl=\pi (7.5)(16.77)\approx 395.1c{m}^2$

Surface area of the cone = $S=L+\pi r^2=395.1+\pi {(7.5)}^2\approx 571.8c{m}^2$

Hence,

L = $395.1c{m}^2$

S = $571.8c{m}^2$