Question

since all circles are similar, a proportion can be set up using the circumference and diameter of each circle. substitute the values $d_1 = 1$, $c_1 = \pi$, and $d_2 = 2r$ into the proportion.$\frac{c_1}{d_1} = \frac{c_2}{d_2}$which shows how to correctly solve for $c_2$, the circumference of any circle with radius $r$?because $\frac{\pi}{1} = \frac{c_2}{2r}, c_2=2r\pi$because $\frac{1}{\pi} = \frac{c_2}{2r}, c_2=\frac{2r}{\pi}$because $\frac{\pi}{2r} = \frac{c_2}{1}, c_2=\frac{\pi}{2r}$because $\frac{\pi}{1} = \frac{c_2}{4r}, c_2=4r\pi$

Explanation:

Step1: Substitute given values

Substitute $C_1=\pi$, $d_1=1$, $d_2=2r$ into $\frac{C_1}{d_1}=\frac{C_2}{d_2}$:
$\frac{\pi}{1}=\frac{C_2}{2r}$

Step2: Solve for $C_2$

Cross-multiply to isolate $C_2$:
$C_2 = \pi \times 2r = 2r\pi$

Answer:

Because $\frac{\pi}{1}=\frac{C_2}{2r}, C_2=2r\pi$