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

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.

Posted by

infoexpert24

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