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?

Solution

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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