Question 94

Find the radius of the circle if the area of its sector is 30.8 sq cm whose corresponding central angle is 72°?

Solution

Let radius = $$r$$ cm and central angle = $$\theta = 72$$°

Area of sector = $$\frac{\theta}{360} \times \pi r^2$$

= $$\frac{72}{360} \times \frac{22}{7} \times (r)^2 = 30.8$$

= $$\frac{1}{5} \times \frac{22}{7} \times (r)^2 = 30.8$$

= $$\frac{22}{7} \times (r)^2 = 30.8 \times 5 = 154$$

=> $$(r)^2 = 154 \times \frac{7}{22} = 49$$

=> $$r = \sqrt{49} = 7$$ cm

=> Ans - (B)

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