Question

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. find: (i) the length of the arc (ii) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chord.

Answer 1

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Answer 2

Answer:

1. The length of the arc = 22cm.
2. The area of the sector formed by the arc = 231cm.
3. Area of the segment formed by the corresponding arc = 40$cm^{2}$

Explanation:

We know,

Radius = 21cm

Angle = 60°

∵ The length of the arc = $\frac{o}{360} 2\pi r$ cm

∴ $\frac{60}{360}$ ×$2$ × $\frac{22}{7}$ × 21 cm

= 22cm.

• Area of the sector formed by the arc =$\frac{o}{360}$ × $\pi r^{2}$

∴ $\frac{60}{360}$ ×$\frac{22}{7}$ × $21^{2}$

= 231 $cm^{2}$

• Area of segment = Area of the sector - Area of triangle

∵ Angle = 60°

∴ It is an equilateral triangle with all sides equal.

Area = $\frac{\sqrt{3} }{4}$ × $21^{2}$

= 190.95 $cm^{2}$

∴ Area of segment = 231 - 190.95 = 40.05 $cm^{2}$

Answer) Area of segment is 40.05 $cm^{2}$