Question

the circumferences of two circles are in the ratio of 2 : 5. the radius of the smaller circle is 16 in. what is the radius of the larger circle? 40 in. 160 in. 32 in. 80 in.

Explanation:

Step1: Relate circumference ratio to radius ratio

Circumference \( C = 2\pi r \), so \( \frac{C_s}{C_l} = \frac{r_s}{r_l} \)

Step2: Set up ratio equation

Given \( \frac{C_s}{C_l} = \frac{2}{5} \), so \( \frac{r_s}{r_l} = \frac{2}{5} \)

Step3: Solve for larger radius \( r_l \)

\( r_l = r_s \times \frac{5}{2} = 16 \times \frac{5}{2} = 40 \)

Answer:

40 in.