Question

The circumference of a circle is 20π. What is the area of the circle?

Answer 1

The area of the circle is 100 square units.

Explanation:

We are given that the circumference of a circle is 20π, and we want to determine its area.

Recall that the circumference of a circle is given by the formula:

`\displaystyle C = 2\pi r`

Substitute:

`20 \pi = 2 \pi r`

Solve for the radius:

`\displaystyle r = (20\pi)/(2\pi) = 10`

The area of a circle is given by:

`\displaystyle A = \pi r^2`

Since the radius is 10 units:

`\displaystyle A = \pi (10)^2`

Evaluate:

`\displaystyle A = 100\pi\text{ units}^2`

In conclusion, the area of the circle is 100 square units.