Question

In a circle of radius $10$ cm, an arc subtends an angle of ${90}^0$ at the centre. Find the area of major sector.

Answer 1

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

$=\frac{22}{7}\times \frac{10\times 10\times 90}{360}$

$\frac{550}{7}$

Area of major sector = area of circle - area of sector OAPB

$=\pi r^2-\frac{550}{7}$

$=\frac{22}{7}\times 10\times 10-\frac{550}{7}$

$=\frac{2200}{7}-\frac{550}{7}$

$=\frac{1650}{7}c{m}^2$