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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Question : A circular arc whose radius is 4 cm makes an angle of 45º at the centre. Find the perimeter of the sector formed. (Take $\pi=\frac{22}{7}$)
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