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# 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

**☛ Related Questions:**

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