Question

two similar circles are shown. the circumference of the larger circle, with radius ob, is 3 times the circumference of the smaller circle, with radius oa. radius ob measures x units. which expression represents the circumference of the smaller circle with radius oa? 2πx units 6πx units (2/3)x units (1/3)x units

Explanation:

Step1: Recall the circumference formula

The circumference formula of a circle is \(C = 2\pi r\). For the larger circle with radius \(OB=x\), its circumference \(C_{B}=2\pi x\).

Step2: Use the relationship between circumferences

Given that \(C_{B} = 3C_{A}\) (where \(C_{A}\) is the circumference of the smaller circle with radius \(OA\)). So \(C_{A}=\frac{C_{B}}{3}\).

Step3: Substitute \(C_{B}\) value

Substitute \(C_{B} = 2\pi x\) into \(C_{A}=\frac{C_{B}}{3}\), we get \(C_{A}=\frac{2\pi x}{3}\).

Answer:

\((\frac{2}{3})\pi x\) units