Question

The radius of a circle is 5 cm. and a circular segmen Subtends an angle 60 degree at the centre. What Is the area of the circular segment​

Answer 1

Answer:

The area of the circle is 10 cm

Answer 2

Answer:

Radius (r) = 5 cm

Angle subtended at centre = 60°

In triangle ABC

AB = AC (radii)

=> <B =<C (Isoceles triangle property)

We know that sum of all angles of triangle = 180°

=> <A + <B + <C = 180

= 60+ <B+<C = 180

<B+<C = 120

2<B = 120

<B=<C = 60   (since <B=<C is proved above)

∴Δ ABC is equilateral.

To find area of circular segment:

(Area of sector- Area of triangle)

Area of sector = (θ/360º) × πr2

                        60/360 x 22/7 x 5x5

                         = 13.09 sq.cm

Area of equilateral triangle = $\frac{\sqrt{3} }{4}$$a^{2}$ =  

                                             10.8 sq.cm

∴Area of segment =  13.09 -10.8 = 2.29 sq.cm