Question

the ratio of the circumferences of two circles is 2:3. if the large circle has a radius of 39 cm, what is the radius of the small circle?
19.5 cm
26 cm
58.5 cm
117 cm

Explanation:

Step1: Recall the formula for circumference

The formula for the circumference of a circle is $C = 2\pi r$. Let the radius of the small - circle be $r_1$ and the radius of the large - circle be $r_2 = 39$ cm. The ratio of the circumferences $C_1:C_2=\frac{2\pi r_1}{2\pi r_2}=\frac{r_1}{r_2}$.

Step2: Set up the ratio equation

We know that $\frac{C_1}{C_2}=\frac{2}{3}$, and since $\frac{C_1}{C_2}=\frac{r_1}{r_2}$, we have the equation $\frac{r_1}{39}=\frac{2}{3}$.

Step3: Solve for $r_1$

Cross - multiply the equation $\frac{r_1}{39}=\frac{2}{3}$ to get $3r_1=2\times39$. Then $3r_1 = 78$. Divide both sides by 3: $r_1=\frac{78}{3}=26$ cm.

Answer:

B. 26 cm