To find the radius of the original circle before dilation, you can use the scale factor. The relationship between the original radius and the new radius after dilation is given by:
\[ \text{New Radius} = \text{Scale Factor} \times \text{Original Radius} \]
Here, the new radius is 18 cm, and the scale factor is 15. Therefore, you can set up the equation:
\[ 18 = 15 \times \text{Original Radius} \]
Now, solve for the original radius:
\[ \text{Original Radius} = \frac{18}{15} \]
Calculating this gives:
\[ \text{Original Radius} = 1.2 \text{ cm} \]
Since none of the provided answers correspond to this outcome, it is possible that I made a calculation error. Let's examine your options again.
Based on the relationship defined earlier, if I consider the possibility that 18 cm is the radius of a circle dilated down from an original, larger radius, then you would have:
\[ \text{Original Radius} = \frac{18}{15} = 1.2 , \text{cm} \]
If instead I consider that the 18 cm is the original radius, considering a dilation that produced a larger circle, with a scale factor of 15, we would find the radius after dilation to be:
\[ 18 \times 15 = 270 , \text{cm} \]
But neither scenario produces answers corresponding to your listed choices of 90 cm, 180 cm, 3.6 cm, or 9 m.
If you intended a different scale factor or radius, could you please clarify? The process in finding the diameter when scaling can lead to multiple configurations based on how the problem was stated.