Chapter 12.3, Problem 4CYU

(a)

To determine

Find the lateral area of the conical tent.

Answer to Problem 4CYU

  $210.5f{t}^2$

Explanation of Solution

Given:

The diameter of the base of the conical tent is 13 ft. and the height is 8 ft.

Formula Used: The Lateral area L of cone with radius r of base is

  $L=\frac{1}{2}Pl=\frac{1}{2}2\pi rl=\pi rl$ , where l is the slant height and P is the perimeter of the base .

Calculation:

diameter = 13 ft.

radius = r = $\frac{13}{2}=6.5ft.$ inches

Use Pythagoras Theorem to find the slant height of the cone = l = $\sqrt{{6.5}^2+8^2}\approx 10.31ft.$

Lateral area of the conical tent = $L=\pi rl=\pi (6.5)(10.31)\approx 210.5f{t}^2$

(b)

To determine

Find the surface area of the conical tent.

Answer to Problem 4CYU

  $343.2f{t}^2$

Explanation of Solution

Formula Used :

The Surface area of a cone :

S = L + B , where L is the lateral area of the cone and B is the area of the base .

Calculation:

From part (a) , Lateral area = L = $210.5f{t}^2$ and the radius = r = 6.5 ft.

The area of the base = B = $\pi r^2=\pi {(6.5)}^2=132.73f{t}^2$

Surface area of the conical tent = S = L + B= $210.5+132.73=343.2f{t}^2$