Question

the figures below are similar.
what is the ratio of the circumference of the smaller circle to the circumference of the larger circle?
write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Explanation:

Step1: Write the formula for circumference

The formula for the circumference of a circle is \(C = 2\pi r\), where \(r\) is the radius.

Step2: Find the circumferences

For the smaller circle with radius \(r_1 = 8\) yd, \(C_1=2\pi\times8 = 16\pi\). For the larger circle with radius \(r_2 = 9\) yd, \(C_2=2\pi\times9 = 18\pi\).

Step3: Calculate the ratio

The ratio of the circumferences is \(\frac{C_1}{C_2}=\frac{16\pi}{18\pi}\). Cancel out \(\pi\) (since \(\pi
eq0\)), we get \(\frac{16}{18}\). Simplify \(\frac{16}{18}\) by dividing numerator and denominator by 2, \(\frac{16\div2}{18\div2}=\frac{8}{9}\).

Answer:

\(8:9\)