### Instruction: The surface area of a particular sphere is $324\pi\text{ cm}^2$. What is the volume, in cubic centimeters, of the sphere? Express your answer in terms of $\pi$.### Response: Let's first find the radius of the sphere.
Ok. I know that the surface area of a sphere is $4\pi r^2$.
That's right. Let's set that equal to $324\pi$.
$4\pi r^2=324\pi$.
We can divide both sides by $4\pi$.
That would give us $r^2=81$.
Now we take the square root of both sides.
So $r=9$.
Now we know that the volume of the sphere is $\frac{4}{3}\pi r^3$.
So if we plug in $9$ for $r$, we get $\frac{4}{3}\pi *9^3$.
$\frac{4}{3}\pi *9^3 = \frac{4}{3}\pi*729$.
$\frac{4}{3}\pi*729=972\pi$.