Question

the area of a circle is 9π square centimeters. what is the diameter? a = 9π cm² give the exact answer in simplest form. centimeters

Explanation:

Step1: Recall area formula

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius. Given $A = 9\pi$, we have $\pi r^{2}=9\pi$.

Step2: Solve for radius

Divide both sides of the equation $\pi r^{2}=9\pi$ by $\pi$. We get $r^{2}=9$. Taking the square - root of both sides, since $r>0$ (radius is non - negative), $r = 3$ cm.

Step3: Calculate diameter

The diameter $d$ of a circle is related to the radius by $d = 2r$. Substituting $r = 3$ cm, we have $d=2\times3=6$ cm.

Answer:

6