To find the radius of the original circle before dilation, you can use the formula:
\[ \text{New Radius} = \text{Scale Factor} \times \text{Original Radius} \]
In this case, the new radius is 18 cm and the scale factor is 15. We can rearrange the formula to find the original radius:
\[ \text{Original Radius} = \frac{\text{New Radius}}{\text{Scale Factor}} = \frac{18 \text{ cm}}{15} \]
Calculating this gives:
\[ \text{Original Radius} = \frac{18}{15} = 1.2 \text{ cm} \]
None of the answer choices provided match this calculation, so let's check if I misinterpreted the question. The answers you provided were:
- 180 cm
- 9 m
- 3.6 cm
- 90 cm
It seems there may have been some confusion. According to the scale factor relationship, if we denote the original radius as R:
\[ 18 \text{ cm} = 15 \times R \]
So,
\[ R = \frac{18 \text{ cm}}{15} = 1.2 \text{ cm} \]
To summarize, the original radius is 1.2 cm, which unfortunately does not appear in the provided options. Please double-check the options or consider clarifying the question or values given.