Question

Find the radius of each circle if the area of the sectoris 12.

a.

b.

Short answer

a. The radius of circle is 5.85 units.

b. The radius of circle is 3.03 units.

Step-by-step solution

a. Step 1. Given information.

Area of sector is 12 units.

Central angle 0.7 rad.

a. Step 2. Write the concept.

Use the given formula to find the radius

Step 3. Determining the radius.

Putting the values in above formula:

$$\begin{gathered} A=\frac{1}{2}{r}^2\theta \\ {r}^2=\frac{2\times 12}{0.7} \\ r=\sqrt{34.28}=5.85 \end{gathered}$$

b. Step 1. Given information.

Area of sector is 12 units.

Central angle 150 degree.

b. Step 2. Write the concept.

First convert given central angle from degree to radian.

$$\begin{gathered} \theta =\frac{150\pi }{180} \\ \theta =\frac{5\pi }{6} \end{gathered}$$

Use the given formula to find the radius

$$\begin{gathered} A=\frac{1}{2}{r}^2\theta \\ {r}^2=\frac{2A}{\theta } \end{gathered}$$

b. Step 3. Determining the radius. 

Putting the values in above formula:

$$\begin{gathered} r^2=\frac{2\times 12}{5\pi /6} \\ {r}^2=\frac{2\times 12\times 6}{5\pi } \\ {r}^2=\frac{144}{5\times 3.14}\left(\because \pi =3.14\right) \\ r=\sqrt{9.17} \\ r=3.03 \end{gathered}$$