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A student measures the circumference of a sector formed by an arc of circle

which forms the angle one radian at its centre as 3 times the radius. Is his
answer correct? Justify.


No, his answer is not justified.

If a sector of radius R forms an angle α radian at the centre, then the circumference is given by
C = αR

So for α=1 radian,
C = 1*R = R
So circumference should be same as radius, not three times radius.

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