Question

the area of a circle is 36π square kilometers. what is the radius? give the exact answer in simplest form. blank kilometers

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 $A = 36\pi$ into the formula:
$36\pi = \pi r^2$

Step3: Solve for $r^2$

Divide both sides by $\pi$:
$\frac{36\pi}{\pi} = \frac{\pi r^2}{\pi}$
$36 = r^2$

Step4: Find radius $r$

Take the positive square root (radius is positive):
$r = \sqrt{36} = 6$

Answer:

6 kilometers