Question

In a circle of diameter 42cm ,if an arc subtends an angle of 60 ˚ at the centre where

∏=22/7, then find the length of the arc.​

Answer 1

Answer :

• The length of arc is 22 cm.

Given :-

• In a circle of diameter 42cm, if an arc subtends an angle of 60° at the centre where π = 22/7.

To Find :-

• Find the length of the arc ?

Solution :-

• Diameter of a circle (d) = 42 cm

Radius of the circle (r) = Diameter/2

➻ r = 42/2

➻ r = 21 cm

• An angle subtends by the arc = (x) = 60° length of the arc (l) = x° × 2πr/360° units.

➻ 60° × 2 × (22/7) × 21/360°

➻ (60° × 2 × 22 × 21)/(7 × 360°)

➻ 2 × 22 × 3/6

➻ 22 cm

• Hence, length of the arc is 22 cm.

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Answer 2

Given:

Diameter = 42 cm

Angle at the centre = 60°

Angle in radian = $\frac{\pi }{180} *60=\frac{\pi }{3} =1.047$

To Find: Length of arc

Calculation:

• Radius of circle is half of diameter = $\frac{42}{2} =21 cm$
• Length of arc = radius X angle at the centre, where r is in radians.

• l = 21 * 1.047

length of arc = 21.987 cm

Answer:

Length of arc is 21.987.