Question

the ratio of the circumferences of two circles is 2:3. If the large circle has a radius of 39 cm, what is the radiusof the small circle?

Answer 1

C1/C2 = 2/3

2pi r1 / 2pi r2 = r1/r2 = 2/3

r1/39 = 2/3

r1 = 39*2/3 = 26

So, your answer is 26cm

Answer 2

`r_(1) = 26`.

Explanation:

Given : the ratio of the circumferences of two circles is 2:3. If the large circle has a radius of 39 cm,

To find : what is the radius of the small circle.

Solution : We have given that ratio of the circumferences of two circles is 2:3.

Let
`r_(2)` is radius of larger circle and
`r_(1)` is radius of small circle .

Then circumference =
`(2\pi\ r_(1) )/(2\pi\ r_(2))` =
`(2)/(3)` .

Solving the above equation

`(r_(1))/(r_(2) )` =
`(2)/(3)` .

We have given radius of larger circle = 39 then

`(r_(1))/(39)` =
`(2)/(3)` .

On multiplying both sides by 39.

`r_(1) = 39 *(2)/(3)`.

`r_(1) = 13 * 2`.

`r_(1) = 26`.

Therefore,
`r_(1) = 26`.