Question

In a circle of radius 14 cm, an arc subtends an angle of ${120}^{\circ }$ at the centre. If $\sqrt{3}$ = 1.73 then the area of the segment of the circle is

(a) $120.56c{m}^2$ (b) $124.63c{m}^2$ (c) $118.24c{m}^2$ (d) $130.57c{m}^2$

Answer 1

Given that, In a circle

Radius = 14 cm

Subtends an angle at the centre = 30°

Area of the segment = $\pi r^2\frac{\theta }{360}$

Area of the sector of angle 120°=

Now
area of req segment = area of the sector - the area of the triangle

area of triangle =

hence area of segment =205.33 - 84.77 = 120.56 $c{m}^2$