To find the radius of a cylinder given its volume and height, 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, and \( h \) is the height.
Given:
- \( V = 1470\pi \) cm³
- \( h = 30 \) cm
We can substitute these values into the formula:
\[ 1470\pi = \pi r^2 (30) \]
Next, we can divide both sides by \( \pi \) (assuming \( \pi \) is not zero):
\[ 1470 = r^2 (30) \]
Now, we can solve for \( r^2 \) by dividing both sides by 30:
\[ r^2 = \frac{1470}{30} \]
Calculating the right-hand side:
\[ r^2 = 49 \]
Now, to find \( r \), we take the square root of both sides:
\[ r = \sqrt{49} = 7 \text{ cm} \]
Thus, the radius of the cylinder is \( \boxed{7} \) cm.