Question

The area of a sector of a circle is 66 cm² and the angle of the sector is 60°. Find the radius of the circle.

• A. $$5\sqrt{21}$$
• B. $$3\sqrt{14}$$
• C. $$3\sqrt{7}$$
• D. $$6\sqrt{14}$$

Answer 1

Answer:

$$3\sqrt{14}$$

The area of a sector of a circle is 66 cm² and the angle of the sector is 60°

Concept used:

Area of a sector = πr² × θ/360°

θ = angle of the sector

r = radius

Calculation:

According to the question,

$60/360\times{\pi{r^2}}=66$

$\pi{r^2}=66\times6$

$22/7\times{r^2}=66\times6$

$r^2=\frac{66\times6\times7}{22}$

$r^2=126$

$r=3\sqrt{14}$