Question

the area of a circle is 100π square feet. what is the radius? give the exact answer in simplest form. feet.

Explanation:

Step1: Recall circle area formula

The area of a circle is $A = \pi r^2$, where $A$ is area and $r$ is radius.

Step2: Substitute given area

Substitute $A = 100\pi$ into the formula:
$100\pi = \pi r^2$

Step3: Cancel $\pi$ from both sides

Divide both sides by $\pi$:
$100 = r^2$

Step4: Solve for radius $r$

Take positive square root (radius is positive):
$r = \sqrt{100} = 10$

Answer:

10 feet