Chapter 8.4, Problem 36AYU

Amount of Material to Make a Tent A cone-shaped tent is made from a circular piece of canvas 24 feet in diameter by removing a sector with central angle $100°$ and connecting the ends. What is the surface area of the tent?

To determine

To find: What is the surface area of the tent?

Answer to Problem 36AYU

Solution:

The surface area of the tent is $326.73$ feet².

Explanation of Solution

Given:

A cone–shaped tent is made from a circular piece of canvas 24 feet in diameter by removing a sector with central angle $100°$ and connecting the ends.

Formula used:

$\text{Area} \text{of} \text{the} \text{sector} = \frac{1}{2}{r}^2\theta$

Calculation:

$\begin{array}{l}\text{Diameter} \text{of} \text{the} \text{canvas}=24 \text{feet},\\ \text{Radius} \text{of} \text{the} \text{canvas}=12 \text{feet}.\end{array}$

Circular piece of canvas 24 feet in diameter is removed.

Hence,

$\theta = 360 - 100 = 260° = 260 * \frac{\pi }{180} = \frac{13\pi }{9}$

$Area of the sector = \frac{1}{2} * {12}^2 * \frac{13\pi }{9}104\pi \approx 326.73 feet$

The surface area of the tent is $326.73$ feet²