To find the radius of the original circle before dilation, you can use the scale factor and the radius of the dilated circle.
The formula relating the original radius (\( r \)) and the dilated radius (\( R \)) is:
\[ R = k \cdot r \]
where \( k \) is the scale factor. In this case, \( R = 18 , \text{cm} \) and \( k = 15 \).
Now, we can rearrange the formula to solve for the original radius \( r \):
\[ r = \frac{R}{k} = \frac{18 , \text{cm}}{15} \]
Calculating this gives:
\[ r = \frac{18}{15} , \text{cm} = \frac{6}{5} , \text{cm} = 1.2 , \text{cm} \]
Thus, the radius of the original circle before dilation is \( 1.2 , \text{cm} \).