Question

In a circle of radius 10 em, a chord subtends an angle of 60° at the centre of the circle. What is the area of the minor segment of the circle correct to one decimal place (π = 3.14)? 
1. 9.4 cm
2. 9.3 cm
3. 9.0 cm
4. 9.2 cm

Answer 1

Correct Answer - Option 3 : 9.0 cm

Given:

The radius of the circle = 10 cm

The subtends an angle θ  = 60° 

Formula used:

The area of the minor segments of the circle = \({r^2}\ \times [{\pi θ \over 360}\ -\ {sin θ\over 2}]\)

Sin60° = √3/2

Calculation:

Let us assume the area of a minor segment of the circle be A

⇒ A =  \({10^2}\ \times [{3.14 \times 60 \over 360}\ -\ {sin 60\over 2}]\)

⇒ A =  \({100}\ \times [{3.14 \ \over 6}\ -\ {1.73\over 4}]\)

⇒ A = \({100}\ \times [{6.28\ -\ 5.19\over 12}]\)

⇒ A = \({100}\ \times [{1.09\over 12}]\ = {100\ \times 0.090}\ =\ 9.0\ cm\)

∴ The required result will be 9 cm.