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Question
A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.
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Solution
Given that circular wire is of radius 3 cm
So when it is cut then its length = 2π × 3 = 6π cm.
Again, it is being placed along a circular hoop of radius 48 cm.
Here, s = 6π cm is the length of arc and r = 48 cm is the radius of the circle.
Therefore, the angle θ, in radian, subtended by the arc at the centre of the circle is given by
θ = `"Arc"/"Radius"`
= `(6pi)/48`
= `pi/8`
= 22.5°.
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