Question

The circumference of a circle is 20π. What is the area of the circle?A. 20πB. 10πC. 100πD. 400π

Answer 1

C. 100π

Step-by-step explanation:

Given:

Circumference of a circle= 20π

Area=?

We find the radius first using the given circumference. The formula is:

C=2πr

Where:

r=radius

C= circumference

Then,

`\begin{gathered} C=2\pi r \\ 20\pi=2\pi r \\ \text{Simplify and rearrange} \\ r=(20\pi)/(2\pi) \\ \text{Calculate} \\ r=10 \end{gathered}`

To get the area of the circle, we use the formula:

`\begin{gathered} A=\pi r^2 \\ We\text{ plug in what we know} \\ A=\pi(10)^2 \\ \text{Simplify} \\ A=100\pi \end{gathered}`

Therefore, the area of the circle is 100π.