Q2 of 18 Page 160

A wire was bent into a circle of diameter 4 centimetres. What would be the diameter of a circle made by bending a wire of half the length?

Diameter of circle = 4 cm


Length of wire = Circumference of circle


If r = radius of circle


Circumference of circle = 2 × π × r=2 × π × 4


=8 × π


If length of wire is halved,


Circumference is also halved


∴ New Circumference = 1/2 × (8 × π)= 4 × π


Let r’be new radius


∴ 2 × π × r'= New Circumference = 4 × π


∴ r’ =


Hence, New diameter = 2 × r'= 2 × 2=4 cm


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