Question

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

Explanation:

Step1: Recall the formula for the circumference of a circle

The formula for the circumference of a circle is \( C = \pi d \), where \( d \) is the diameter of the circle.

Step2: Find the circumference of the larger circle

The diameter of the larger circle is \( 4 \) inches. Using the formula \( C = \pi d \), the circumference \( C_{large} = \pi \times 4 = 4\pi \) inches.

Step3: Find the circumference of the smaller circle

The diameter of the smaller circle is \( 2 \) inches. Using the formula \( C = \pi d \), the circumference \( C_{small} = \pi \times 2 = 2\pi \) inches.

Step4: Find the ratio of the circumferences

The ratio of the circumference of the larger circle to the smaller circle is \( \frac{C_{large}}{C_{small}}=\frac{4\pi}{2\pi} \). The \( \pi \) terms cancel out, leaving \( \frac{4}{2} = 2:1 \).

Answer:

\( 2:1 \)