To find the radius \( r \) of the cylinder, we will use the formula for the volume of a cylinder:
\[ V = \text{Area of base} \cdot \text{Height} = \pi r^2 \cdot h \]
We know from the problem that:
- The volume \( V = 640\pi \)
- The height \( h = 10 \)
We can rearrange the formula to solve for the radius \( r \):
\[ V = \pi r^2 \cdot h \] Substituting in the values we have:
\[ 640\pi = \pi r^2 \cdot 10 \]
Now, divide both sides by \( \pi \):
\[ 640 = r^2 \cdot 10 \]
Next, divide both sides by 10 to isolate \( r^2 \):
\[ r^2 = \frac{640}{10} \] \[ r^2 = 64 \]
Now take the square root of both sides to find \( r \):
\[ r = \sqrt{64} \] \[ r = 8 \]
Thus, the radius of the cylinder is \( r = 8 \).
So, the final answer is: \[ \boxed{8} \]