Question 57

The area of a sector of a circle with central angle $$60^\circ$$ is A. The circumference of the circle is C. Then A is equal to:

Solution

Area of the sector with central angle $$\theta=\frac{\theta}{360}\times\pi^{2}$$

Area = $$\frac{60}{360}\times\pi^{2}= \frac{\pi r^{2}}{6}$$--------i

Circumference of the circle $$C=2\pi r$$ --------ii

From i,$$ A=\frac{\pi r^{2}}{6} = \frac{4\pi.\pi^{2}}{6.4\pi}$$ ( numerator and denominator multiplied by $$4\pi$$ )

So,$$ A = \frac{(2\pi r)^{2}}{24\pi}=\frac{C^{2}}{24\pi}$$---(From ii)

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