To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
where:
- \(V\) is the volume,
- \(r\) is the radius,
- \(h\) is the height.
Given that the volume \(V = 972\pi\) cm³ and the height \(h = 27\) cm, we can plug these values into the formula:
\[ 972\pi = \pi r^2 (27) \]
First, we can divide both sides by \(\pi\):
\[ 972 = 27r^2 \]
Next, we solve for \(r^2\) by dividing both sides by 27:
\[ r^2 = \frac{972}{27} \]
Calculating \(972 \div 27\):
\[ 972 \div 27 = 36 \]
So, we have:
\[ r^2 = 36 \]
To find \(r\), we take the square root of both sides:
\[ r = \sqrt{36} = 6 \]
Thus, the radius of the cylinder is
\[ \boxed{6} \text{ cm}. \]