Question : The area of a sector of a circle is 88 sq. cm., and the angle of the sector is 45°. Find the radius of the circle. (Use $\pi=\frac{22}{7}$)
Option 1: $3 \sqrt{ 11} \mathrm{~cm}$
Option 2: $4 \sqrt{ 14} \mathrm{~cm}$
Option 3: $6 \sqrt{ 13} \mathrm{~cm}$
Option 4: $5 \sqrt{ 14} \mathrm{~cm}$
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Correct Answer: $4 \sqrt{ 14} \mathrm{~cm}$
Solution :
Given, that the angle of the sector is 45°.
The area of a sector of a circle is 88 sq. cm.
Let the radius of the circle be $r$ cm.
We know that Area of sector = $\frac{\theta}{360^{\circ}}\times \pi r^2$
According to the question,
$\frac{\theta}{360^{\circ}}\times \pi r^2=88$
⇒ $\frac{22}{7}\times r^2\times \frac{45}{360}=88$
⇒ $r^2=224$
$\therefore r=4\sqrt{14} \mathrm{~cm}$
Hence, the correct answer is $4 \sqrt{ 14} \mathrm{~cm}$.
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