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a piece of wire is 20 cm long bent into the form of an arc of a circle subtending an angle of 60 at its center. the radius of the circle is (1). Options a) 20/6+πcm b) 30/6+πcm c) 60/6+πcm d) 15/6+πcm

Posted by Rajeevan Rajkumar 4 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 4 years, 9 months ago

In the question, we have to find the radius (r) of the circle.
We are given that a piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of 60 degrees at its centre. So, here the arc length will be the same as 20 cm, as shown in the figure below.

Next, we know the arc length formula as arclength=θ360o×(2πr)arclength=θ360o×(2πr), here θθ is the angle subtended at the centre of the circle. So we have: θ=60oθ=60o and arclength=20cmarclength=20cm. So using the formula we will find the radius of the circle, as shown below:
⇒arclength=θ360o×(2πr)⇒20=60o360o×(2πr)⇒20=16×(2πr)⇒60=(πr)⇒r=60π⇒arclength=θ360o×(2πr)⇒20=60o360o×(2πr)⇒20=16×(2πr)⇒60=(πr)⇒r=60π
So we get the required radius of the circle as r=60πcmr=60πcm.

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