Question
scale factor of 1/5 to create a circle with a radius of 18cm. what is the radius of the original circle you dilated
Answers
GPT-4o mini
To find the radius of the original circle before applying the scale factor of \( \frac{1}{5} \), you can set up the equation based on the relationship between the original radius and the radius after dilation.
Let \( r \) be the radius of the original circle. When you apply a scale factor of \( \frac{1}{5} \), the new radius becomes:
\[
\text{New radius} = \text{Original radius} \times \text{Scale factor} = r \times \frac{1}{5}
\]
You are given that the new radius is \( 18 \, \text{cm} \). Therefore, you can set up the equation:
\[
r \times \frac{1}{5} = 18
\]
To solve for \( r \), multiply both sides of the equation by \( 5 \):
\[
r = 18 \times 5 = 90 \, \text{cm}
\]
Thus, the radius of the original circle is \( 90 \, \text{cm} \).
Let \( r \) be the radius of the original circle. When you apply a scale factor of \( \frac{1}{5} \), the new radius becomes:
\[
\text{New radius} = \text{Original radius} \times \text{Scale factor} = r \times \frac{1}{5}
\]
You are given that the new radius is \( 18 \, \text{cm} \). Therefore, you can set up the equation:
\[
r \times \frac{1}{5} = 18
\]
To solve for \( r \), multiply both sides of the equation by \( 5 \):
\[
r = 18 \times 5 = 90 \, \text{cm}
\]
Thus, the radius of the original circle is \( 90 \, \text{cm} \).