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

Question

asked Dec 3, 2022 225k views

1 Answer

Likan Zhan · Answer 1 · 2022-12-08T08:56:46+0000

Answer:

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.