To find the radius of the original circle before dilation, you can use the relationship between the scale factor and the radius of the dilated circle.
The formula to find the radius of the original circle (r_original) is:
\[ r_{original} = \frac{r_{dilated}}{scale\ factor} \]
Given:
- \( r_{dilated} = 18 , \text{cm} \)
- \( scale\ factor = 15 \)
Now substitute the values into the formula:
\[ r_{original} = \frac{18 , \text{cm}}{15} \]
Calculating this gives:
\[ r_{original} = \frac{18}{15} = 1.2 , \text{cm} \]
Thus, the radius of the original circle is 1.2 cm.