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
Is there an error in this question or solution?