Q3 of 18 Page 173

From a bangle of radius 3 centimetres, a piece is to be cut out to make a ring of radius centimetres.

i) What should be the central angle of the piece to be cut out?


ii) The remaining part of the bangle was bent to make a smaller bangle. What is its radius?

i) Radius of bangle = 3 cm


Radius of ring =


If r = radius of circle


Circumference of circle = 2 × π × r cm


∴ Length of ring = 2 × π × = π cm


Hence, length of arc = π cm


In a circle of radius r,


If central angle = x°


Length of arc =


Here r = 3 cm


π =


∴ = x


∴ x =


ii) Length of remaining part = Length of bangle-Length of smaller part


= (2 × π × 3)-(π)


= 5 × π ≈15.7 cm


Let a be the new radius


Since,


Circumference = 2 × π × a


15.7 = 2 × π × a


∴ a =


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1

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