The radii of two circles are in the ratio 3:5

The radius of two circles are in the ratio 3: 5, find the ratio between their circumferences.

The ratio of the radius of the circles = 3: 5

Let the radius of the first circle = 3x
and radius of the second circle = 5x

∴ Circumference of the first circle = 2πr

= 2π × 3x = 6πx

and circumference of the second circle = 2πr

= 2π × 5x = 10x

∴ The ratio between their circumference= 6πx : 10πx= 16 : 10

= 3 : 5

Concept: Circumference of a Circle

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Page 2

The circumferences of two circles are in the ratio 5: 7, find the ratio between their radius.

The ratio of the circumference of the circle = 5: 7

Let circumference of the first ratio = 5x

∴ 2πr = 5x

⇒ r =`(5"x")/(2π)`

and the circumference of the second ratio = 7x

∴ 2πr = 7x

⇒ r = `(7"x")/(2π)`

The ratio between their radius =`(5"x")/(2π):(7"x")/(2π)`

= 5: 7

Concept: Circumference of a Circle

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