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Areas of two circles are equal. Is it necessary that their circumferences are equal? Why?

Answers (1)

True

Solution

Use area of circle \pi r^{2}

Let two circles having radius r1  and r2

Here it is given that their areas are equal

\pi r_{1}^{2}=\pi r_{2}^{2}\\ \\ r_{1}^{2}= r_{2}^{2}\\ \\ r_{1}= r_{2}\\

We know that circumference of circle =2\pi r

Circumference of circle with radius r1 = 2πr1

Circumference of circle with radius r2 = 2πr2    …..(1)

Put r2 = r1 in (1) we get

2πr1 = 2πr2

Hence the circumference of given circle are also equal because two circles with equal radii will also have equal circumference.                               

Therefore, the given statement is True.

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