Question

Find the area of the major segment APB of a circle of radius 35 cm and $\angle$AOB = 90 ${}^{\circ }$, as shown in the given figure.

Answer 1

Radius of circle = 35 cm
Area of major segment = Area of right angled triangle +(270/360)Area of circle

Area of major segment = area of triangle + $\frac{3}{4}\times$ area of circle =$\frac{1}{2}\times height\times base+\frac{3}{4}\times \pi \times r^2=\frac{1}{2}\times r\times r+\frac{3}{4}\times \pi \times r^2=\left(\frac{2+3\pi }{4}\right)r^2$

putting r=35 cm and $\pi =\frac{22}{7}$ , we get

Area of major segment = 3500 cm²