Question

the figures below are similar. the circumference of each figure is given.

$c_1 = 13$ in

$c_2 = 25$ in

what is the ratio of the radius of the smaller circle to the radius of the larger circle?

write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Recall circumference formula

The circumference of a circle is $C = 2\pi r$, where $r$ is the radius.

Step2: Solve for radii of both circles

For the smaller circle: $r_1 = \frac{C_1}{2\pi} = \frac{13}{2\pi}$
For the larger circle: $r_2 = \frac{C_2}{2\pi} = \frac{25}{2\pi}$

Step3: Compute the ratio $r_1:r_2$

$$\frac{r_1}{r_2} = \frac{\frac{13}{2\pi}}{\frac{25}{2\pi}} = \frac{13}{25}$$

Answer:

13:25