Question

In a Circle of radius 6 cm, a chord of length 10 cm makes an angle of 110degree at the centre of circle. Find the:-


The circumference of the circle

the area of thr circle

The length of the arc AB

the area of th sector OAB.

Answer 1

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Answer 2

Length of the chord of circle = 10cm (Given)

Radius of circle = r = 6 cm (Given)

Angle at the centre of the circle = 110° (Given)

1. Circumference of a circle

= C = 2πr  

C = 2 × 22/7 × 6  

C = 264/7  

C = 37.71 cm

Thus, the circumference of a circle = 37.71 cm

2. Area of a circle,

A = πr²

A = 22/7 × 6²

A = 22/7 × 36

A = 113.1 cm²

Thus, area of a circle = 113.1 cm²

3. Length of an arc

l = (θ/360) × 2πr

l = (110/360) × 2 × 22/7 × 6

l = 11/36 × 44/7  ×6

l = 484/ 6×7 = 484/42  

l = 11.52 cm

Thus, the length of an arc AB is 11.52 cm

4. Area of the sector of a circle

AOB = (θ/360) × πr²

= (110/360) × 22/7  ×6²

= 11/36 × 22/7  × 36

= (11 × 22 ) /7  

= 34.5 cm²

Thus, the area of sector of a Circle ,AOB is 34.5 cm²