Circumferences of two circles are equal. Is it necessary that their areas be equal? Why
Solution:
Consider C1 and C2 as the two circles of radius r1 and r2
Circumference of circle C1 = 2πr1
Circumference of circle C2 = 2πr2
It is given that
Circumferences of two circles are equal
2πr1 = 2πr2
It is possible if the radius of both the circles are same
r1 = r2 = r
A1 = πr1²
Area of circle C2
A2 = πr2²
Dividing the area
A1/A2 = πr1²/πr2² = r²/r² = 1
A1 = A2 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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