Question : The area of a sector of a circle is 616 cm2 with a central angle of 10°. The radius of the circle is_____.
(use $\pi=\frac{22}{7}$)
Option 1: 84 cm
Option 2: 21 cm
Option 3: 48 cm
Option 4: 28 cm
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Correct Answer: 84 cm
Solution :
The area of a sector of a circle is 616 cm
2
with a central angle of 10°.
Let the radius of the circle = $r$ cm
We know,
The area of a sector of a circle with a central angle of $\theta=(\pi r^2×\frac{\theta}{360^\circ})$
According to the question,
$(\pi r^2×\frac{10^\circ}{360^\circ})=616$
$⇒\frac{22}{7}×r^2×\frac{10^\circ}{360^\circ}=616$
$⇒r^2=616×\frac{7}{22}×\frac{360^\circ}{10^\circ}$
$⇒r=\sqrt{7056}$
$\therefore r=84$ cm
Hence, the correct answer is 84 cm.
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