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 radius of the

small circle?
19.5 cm
26 cm
58.5 cm
117 cm

Answer 1

Option B: 26cm is the radius of smaller circle.

Explanation:

Given that:

Ratio of circumferences of two circles = 2:3

We know that circumference of circle is given by 2πr.

Radius of larger circle =
`r_(2)` = 39 cm

Radius of smaller circle =
`r_(1)`

Now,

`(2\pi r_1)/(2\pi r_2)=(2)/(3)\\(r_1)/(r_2)=(2)/(3)`

Putting radius of larger circle

`(r_1)/(39)=(2)/(3)\\\\r_1=(2)/(3)*39\\\\r_1=26`

Therefore,

The radius of smaller circle is 26cm.

Hence,

Option B: 26cm is the radius of smaller circle.