Question

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

$c_1 = 38$ ft
$c_2 = 44$ ft

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 the circumference formula

The circumference formula of a circle is \(C = 2\pi r\). For the first circle \(C_1=2\pi r_1 = 38\), so \(r_1=\frac{38}{2\pi}\). For the second circle \(C_2 = 2\pi r_2=44\), so \(r_2=\frac{44}{2\pi}\).

Step2: Calculate the ratio of radii

The ratio of the radii \(\frac{r_1}{r_2}=\frac{\frac{38}{2\pi}}{\frac{44}{2\pi}}\). The \(2\pi\) terms cancel out, and we get \(\frac{38}{44}\). Simplify \(\frac{38\div2}{44\div2}=\frac{19}{22}\).

Answer:

\(19:22\)