Find the area of the sector of a circle of radius 7 cm

Find the area of the sector of a circle of radius 7 cm and of central angle 90°. Also, find the area of corresponding major sector.

Answer

r = 7 cm, θ = 90°

Area of sector

$$ \frac{πr^2θ}{360} =\frac{22}{7} \times 7 \times 7 \times \frac{90}{360} $$

$$ = \frac{77}{2} cm^2 $$

$$ = 38.5 cm^2 $$

$$ \text{Area of circle} = πr^2 = \frac{22}{7} \times 7 \times7 = 154 cm^2 $$

$$ \text{Area of major sector} = 154 - 38·5 = 115.5 cm^2 $$