Question

the ratio of the radii of two circles is 4 : 5. what is the ratio of the circumferences of the two circles? options: 4π:5, π:5, 16:25, 4:5 (from the boxes in the image)

Explanation:

Step1: Define radii ratio

Let radii be \( r_1 = 4k \), \( r_2 = 5k \)

Step2: Circumference formula

\( C = 2\pi r \)

Step3: Calculate circumferences

\( C_1 = 2\pi(4k) = 8\pi k \), \( C_2 = 2\pi(5k) = 10\pi k \)

Step4: Find ratio

\( C_1:C_2 = 8\pi k:10\pi k = 4:5 \)

Answer:

4:5