Question : The area of a sector is 1848$\mathrm{~m}^2$ and the central angle of the sector is $270°$. Find the radius of the circle. (Take $\pi=\frac{22}{ 7}$)
Option 1: 784 m
Option 2: 22 m
Option 3: 27 m
Option 4: 28 m
Correct Answer: 28 m
Solution :
Given: Central angle of the sector = 270°
Area of given sector = 1848 m
2
We know, area of a sector = $\frac{\theta}{360°}\times{\pi r^2}$
So, $\frac{270°}{360°}\times{\frac{22}{7} r^2}=1848$
⇒ $ r^2=1884\times\frac{4}{3}\times\frac{7}{22}$
⇒ $r^2 = 28\times 28$
⇒ $r=28$ m
Hence, the correct answer is 28 m.
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