To find the radius of the original circle before dilation, you can use the formula for dilation, which states:
\[ \text{New radius} = \text{Original radius} \times \text{Scale factor} \]
In this case, you have the new radius as 18 cm and the scale factor as \( \frac{1}{5} \). You can rearrange the formula to find the original radius:
\[ \text{Original radius} = \frac{\text{New radius}}{\text{Scale factor}} \]
Substituting in the known values:
\[ \text{Original radius} = \frac{18 \text{ cm}}{1/5} = 18 \text{ cm} \times 5 = 90 \text{ cm} \]
Therefore, the radius of the original circle you dilated is 90 cm.