Question : The area of a sector of a circle is 110 cm2 and the central angle of the sector is 56°, what is the circle's radius? (Take $\pi=\frac{22}{7}$)
Option 1: 35 cm
Option 2: 20 cm
Option 3: 25 cm
Option 4: 15 cm
Correct Answer: 15 cm
Solution :
Given: The area of a sector of a circle = 110 cm²
The central angle of the sector = 56°
Now, Area of sector in a circle $= \frac{\theta}{360}\times {\pi} r^2 $, where $\theta$ is the central angle in degrees
$\therefore 110= \frac{22}{7}\times\frac{56}{360}\times r^2$
⇒ $5=\frac{8}{360}\times r^2$
⇒ $r^2=225$
⇒ $r = 15$ cm
Hence, the correct answer is 15 cm.
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