To find the radius of the cylinder, we can start from the volume formula you provided:
\[ V = \text{Area of base} \cdot \text{Height} \] \[ V = \pi r^2 \cdot h \]
We know:
- Volume \( V = 125\pi \)
- Height \( h = 5 \)
Now, we can substitute the known values into the formula:
\[ 125\pi = \pi r^2 \cdot 5 \]
First, we can divide both sides of the equation by \( \pi \):
\[ 125 = r^2 \cdot 5 \]
Next, we can divide both sides by 5 to isolate \( r^2 \):
\[ r^2 = \frac{125}{5} \] \[ r^2 = 25 \]
Now, we take the square root of both sides to find \( r \):
\[ r = \sqrt{25} \] \[ r = 5 \]
Therefore, the radius \( r \) of the cylinder is:
\[ r = 5 \text{ units} \]