Question

the figures below are similar.
if the ratio of the circles circumferences is 2:1, what is n?
n = \boxed{} meters

Explanation:

Step1: Recall the circumference formula

The circumference of a circle is \(C = \pi d\), where \(d\) is the diameter.

Step2: Set up the ratio

Let \(C_1=\pi\times8\) (for the first circle with diameter \(8\)) and \(C_2 = \pi\times n\) (for the second circle with diameter \(n\)). The ratio \(\frac{C_1}{C_2}=\frac{2}{1}\). Substitute \(C_1\) and \(C_2\): \(\frac{\pi\times8}{\pi\times n}=\frac{2}{1}\).

Step3: Simplify the equation

Cancel out \(\pi\) (since \(\pi
eq0\)), we get \(\frac{8}{n}=\frac{2}{1}\). Cross - multiply: \(2n = 8\).

Step4: Solve for \(n\)

Divide both sides by \(2\): \(n=\frac{8}{2}=4\).

Answer:

\(4\)