Q. 49 - Precalculus Enhanced with Graphing Utilities

Question

Find the length of the arc subtended by a central angle of $30°$ on a circle of radius $2$ feet. What is the area of the sector?

Step-by-Step Solution

Answer

The area is $1.05f{t}^2$

Step 1: Given information

Given central angle of ${30}^{\circ }$ and radius of $2ft$

Step 2: Use the formula and calculate

Calculating, we get

$$\begin{gathered} s=r\theta \\ s=\left(2\mathrm{ft}\right)\left(30°·\frac{\pi }{180°}\right) \\ s=\frac{\pi }{3}\mathrm{ft} \\ s=1.05ft \end{gathered}$$

Step 3: Use the formula for area and calculate

Calculating, we get

$$\begin{gathered} A=\frac{1}{2}(2\mathrm{ft}{)}^2\left(30°·\frac{\pi }{180°}\right) \\ A=\frac{\pi }{3}{\mathrm{ft}}^2 \\ A=1.05f{t}^2 \end{gathered}$$