To find the radius of the original circle before dilation, you can use the relationship between the original radius \( r \) and the scaled radius \( R \) with the scale factor \( k \):
\[ R = k \times r \]
In this case, \( R = 18 \) cm and \( k = 15 \). Rearranging the formula to solve for \( r \):
\[ r = \frac{R}{k} = \frac{18 \text{ cm}}{15} = 1.2 \text{ cm} \]
After checking the options provided, it seems there are no direct matches to the answer calculated. Let's denote the calculated radius again as 1.2 cm, which is a discrepancy with the provided choices (180 cm, 9 m, 3.6 cm, 90 cm).
Let's examine your inputs again; based on the scale factor of 15, the original radius must have been smaller. Considering the scale factor applies a change from the original to the dilated circle, the expected value according to the problem statement does not seem feasible with a 15x scale factor and a resulting radius of 18 cm.
If the original radius is indeed confirmed as 1.2 cm based on dilation, and you are looking only at the listed choices, it appears there may be an either error in the setup of your question or in the list of responses because 1.2 cm (the correct original radius based on your provided circle) does not match any of the given answer choices.
To clarify based on the question on its own merit, your output results in a radius of:
\( r = 1.2 \text{ cm} \)
I recommend double-checking the input values or specifying the question further for appropriate understanding!
1 answer