Question 80

What is the measure of the central angle of the sector whose area is 462 sq cm and radius of the circle is 21 cm?

Let central angle = $$\theta$$ and radius = 21 cm

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

= $$\frac{\theta}{360} \times \frac{22}{7} \times (21)^2 = 462$$

= $$\frac{\theta}{360} \times 22 \times 63 = 462$$ 

= $$\frac{\theta}{20} \times 77 = 462$$

=> $$\theta = \frac{462}{77} \times 20$$

=> $$\theta = 6 \times 20 = 120$$°

=> Ans - (D)

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