Question

The area of a sector of a circle is 88 cm2 and the angle of the sector is 120°. Find the radius of the circle.

• A. $$12\sqrt{2}$$
• B. 8.4 cm
• C. $$2\sqrt{21}$$
• D. $$6\sqrt{14}$$

Answer 1

Answer:

$$2\sqrt{21}$$

Area of a sector = πr² × θ/360°

θ = angle of the sector

r = radius

Calculation:

According to the question,

$120/360\times{\pi{r^2}}=88$

$\pi{r^2}=88\times3$

$22/7\times{r^2}=88\times3$

$r^2=\frac{88\times3\times7}{22}$

$r=2\sqrt{21}$