The areas of two circles are in the ratio 49:64. Find the ratio of their circumferences.
Solution:
Let there be two circles of radius r₁ and r₂.
The area of the two circles are therefore πr₁² and πr₂²
It is given that their areas are in the ratio 49:64, therefore we can write,
πr₁²/πr₂² = 49/64
r₁²/r₂² = 49/64
r₁/r₂ = 7/8
Circumference of the circle = 2πr
Circumference of the two circles are 2πr₁ and 2πr₂ respectively. Therefore the ratio of the circumferences is:
2πr₁/ 2πr₂ = r₁/r₂ = 7/8
✦ Try This: The areas of two circles are in the ratio 25:36. Find the ratio of their circumferences.
Let there be two circles of radius r₁ and r₂.
The area of the two circles are therefore πr₁² and πr₂²
It is given that their areas are in the ratio 49:64, therefore we can write,
πr₁²/πr₂² = 25/36
r₁²/r₂² = 25/36
r₁/r₂ = 5/6
Circumference of the circle = 2πr
Circumference of the two circles are 2πr₁ and 2πr₂ respectively. Therefore the ratio of the circumferences is:
2πr₁/ 2πr₂ = r₁/r₂ = 5/6
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 69
The areas of two circles are in the ratio 49:64. Find the ratio of their circumferences.
Summary:
The areas of two circles are in the ratio 49:64. The ratio of their circumferences is 7:8
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