To find the radius of the original circle before dilation, you can use the formula for dilation which is:
\[ \text{New Radius} = \text{Scale Factor} \times \text{Original Radius} \]
In this case, the new radius (after dilation) is 18 cm, and the scale factor is 15. We can rearrange the formula to find the original radius:
\[ \text{Original Radius} = \frac{\text{New Radius}}{\text{Scale Factor}} \]
Substituting the known values:
\[ \text{Original Radius} = \frac{18 \text{ cm}}{15} = 1.2 \text{ cm} \]
However, none of the given responses match this calculation directly. Let's check the options provided:
- 180 cm
- 90 cm
- 3.6 cm
- 9 m
It seems there may have been an error in formulating the responses or in the interpretation of the scale factor. Based on common dilation coefficients, if we were seeking a radius that would produce one close to the original radius, you might consider typical scenarios leading to assumptions about real-world contexts.
But from the calculations performed, the original radius should indeed be 1.2 cm, which again does not match with any of the listed options. Please double-check the question or provide any additional context if available.