Question

the ratio of the radii of two circles is 4:5. what is the ratio of the circumferences of the two circles?
16:25
π:5
4π:5
4:5

Explanation:

Step1: Recall the circumference formula

The formula for the circumference of a circle is $C = 2\pi r$.

Step2: Let the radii be $4x$ and $5x$

Let the radii of the two circles be $r_1 = 4x$ and $r_2=5x$.

Step3: Calculate the circumferences

$C_1 = 2\pi r_1=2\pi(4x) = 8\pi x$ and $C_2 = 2\pi r_2=2\pi(5x)=10\pi x$.

Step4: Find the ratio of the circumferences

$\frac{C_1}{C_2}=\frac{8\pi x}{10\pi x}=\frac{4}{5}$.

Answer:

D. 4:5