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  • The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?

The numerical value of the area of a circle is greater than the numerical value of its circumference. Is this statement true? Why?

Answers (1)

False

Solution

Area of circle =\pi r^{2}

Circumference of circle =2\pi r

Case 1:

Let r = 1

Area of circle =\pi r^{2}=\pi(1)^{2}=\pi

Circumference of circle = 2\pi r= 2\pi (1)=2 \pi

Case 2:

Let r = 3

Area of circle = πr2 = π(3)2 = 9π

Circumference of circle = 2πr = 2π(3) = 6π

Conclusion:- In case (1) we found that the area is less than the circumference but in case (2) we found that the area is greater than the circumference.

So, from conclusion we observe that it depend on the value of radius of the circle.

Hence the given statement false.

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infoexpert24

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