Question

Q.In a circle of radius 6cm,a chord of length 10cm makes an angle of 110° at the centre of the circle.Find:
(i) the circumference of the circle,
(ii) the area of the circle,
(iii) the length of the arc AB,
(iv) the area of the sector OAB.​

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Answer 1

$\small \mathsf\pink{Given:}$

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

$\small \mathsf\green{Thus, \: the \: circumference \: of \: a \: circle = 37.71 cm}$

2. Area of a circle,

A = πr²

A = 22/7 × 6²

A = 22/7 × 36

A = 113.1 cm²

$\small \mathsf\green{Thus, \: area \: of \: a \: circle = 113.1 cm²}$

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

$\small \mathsf\green{Thus, \: the \: length \: of \: an \: arc \: AB \: is \: 11.52 cm}$

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

$\small \mathsf\green{Thus \: , the \: area \: of \: sector \: of \: a \: Circle , \: AOB \: is \: 34.5 cm²}$