Question

the figures below are similar.
what is the ratio of the area of the smaller circle to the area 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 area formula for a circle

The area of a circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Find the area of the smaller circle

The radius of the smaller circle (\( r_1 \)) is \( 5 \) cm. Using the area formula, the area (\( A_1 \)) is \( \pi \times (5)^2 = 25\pi \) square cm.

Step3: Find the area of the larger circle

The radius of the larger circle (\( r_2 \)) is \( 6 \) cm. Using the area formula, the area (\( A_2 \)) is \( \pi \times (6)^2 = 36\pi \) square cm.

Step4: Find the ratio of the areas

The ratio of the area of the smaller circle to the area of the larger circle is \( \frac{A_1}{A_2} = \frac{25\pi}{36\pi} \). The \( \pi \) terms cancel out, leaving \( \frac{25}{36} \), which as a ratio is \( 25:36 \).

Answer:

25:36