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

Answer:

$r_{1} = 26$.

Step-by-step 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 = $\frac{2\pi\ r_{1} }{2\pi\ r_{2}}$ = $\frac{2}{3}$ .

Solving the above equation

$\frac{r_{1}}{r_{2} }$ =  $\frac{2}{3}$ .

We have given radius of larger circle = 39 then

$\frac{r_{1}}{39}$ =  $\frac{2}{3}$ .

On multiplying both sides by 39.

$r_{1} = 39 *\frac{2}{3}$.

$r_{1} = 13 * 2$.

$r_{1} = 26$.

Therefore, $r_{1} = 26$.