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

**Solution:**

Consider C_{1} and C_{2} as the two __circles__ of radius r_{1} and r_{2}

__Circumference of circle__ C_{1} = 2πr_{1}

Circumference of circle C_{2} = 2πr_{2}

It is given that

Circumferences of two circles are equal

2πr_{1} = 2πr_{2}

It is possible if the radius of both the circles are same

r_{1} = r_{2} = r

__Area of circle__ C_{1}

A_{1} = πr_{1}²

Area of circle C_{2}

A_{2} = πr_{2}²

Dividing the area

A_{1}/A_{2} = πr_{1}²/πr_{2}² = r²/r² = 1

A_{1} = A_{2} which means that the areas are equal

Therefore, the statement is true.

**✦ Try This:** Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.2 Problem 12**

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

**Summary:**

The statement “Circumferences of two circles are equal. Is it necessary that their areas be equal” is true

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