Question

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

Explanation:

Step1: Recall circle - area formula

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius. Given $A = 100\pi$.

Step2: Solve for the radius

Set $\pi r^{2}=100\pi$. Divide both sides of the equation by $\pi$:
$r^{2}=\frac{100\pi}{\pi}=100$. Then take the square - root of both sides. Since $r>0$ (radius is a non - negative quantity), $r = 10$ cm.

Step3: Calculate the diameter

The diameter $d$ of a circle is related to the radius by the formula $d = 2r$. Substitute $r = 10$ into the formula, we get $d=2\times10 = 20$ cm.

Answer:

20