Question

The area of a circle is $25\pi$square centimeters. What is the circumference?

(F) $62.5\pi \mathrm{cm}$

(G) $50\pi \mathrm{cm}$

(H) $5\pi \mathrm{cm}$

(J) $10\pi \text{cm}$

Short answer

The option J. $10\pi \text{cm}$is correct.

Step-by-step solution

Step-1. Write down the given statement.

The area of circle is $25\pi \text{squarecm}$.

Step-2. By formula of area of circle evaluate radius of circle.

The formula for area of circle is$\pi r^2$ where (r) is radius of circle.

So, we can find the radius of the circle as:

$\begin{array}{c}\pi r^2=25\pi \\ r^2=25\\ r=\sqrt{25}\\ r=5\text{cm}\end{array}$

Step-3. Evaluate circumference of circle.

Now, put the value of r (radius) in the formula of circumference of circle.

$\begin{array}{l}=2\pi r\\ =2\pi \left(5\right)\\ =10\pi \text{cm}\end{array}$

Hence option (J)$10\pi \text{cm}$ is correct.