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?
32 in.
40 in.
80 in.
160 in.

Explanation:

Step1: Recall the circumference formula

The formula for the circumference of a circle is $C = 2\pi r$. Let the radius of the smaller circle be $r_1 = 16$ in and its circumference be $C_1$, and the radius of the larger circle be $r_2$ and its circumference be $C_2$. We know that $\frac{C_1}{C_2}=\frac{2}{5}$. Since $C_1 = 2\pi r_1$ and $C_2=2\pi r_2$, then $\frac{C_1}{C_2}=\frac{2\pi r_1}{2\pi r_2}=\frac{r_1}{r_2}$.

Step2: Set up the proportion

We have $\frac{r_1}{r_2}=\frac{2}{5}$, substituting $r_1 = 16$ in, we get $\frac{16}{r_2}=\frac{2}{5}$.

Step3: Cross - multiply and solve for $r_2$

Cross - multiplying gives $2r_2=16\times5$. So $2r_2 = 80$, and then $r_2=\frac{80}{2}=40$ in.

Answer:

B. 40 in.