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  • Circumferences of two circles are equal. Is it necessary that their areas be equal? Why?

Circumferences of two circles are equal. Is it necessary that their areas be equal? Why?

Answers (1)

True

Solution

Use circumference of circle =2 \pi r

Let two circles having radius r1  and r2 

Here it is given that their circumferences are equal

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

We know that area of circle = \pi r^{2}

Area of circle with radius r1 = πr12

Area of circle with radius r2 = πr22     ……..(1)

Put r2 = r1   in (1) we get

πr22 = πr12

Hence the area of given circles are also equal because two circles with equal radii will also have equal areas.

Hence the given statement is True.

Posted by

infoexpert24

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