Question
Used a Scale factor of ⅔ to dilate a circle with radius of 18cm. What is radius or original circle?
Answers
GPT-4o mini
To find the radius of the original circle given that the circle was dilated with a scale factor of \( \frac{2}{3} \) and the radius of the dilated circle is 18 cm, you can use the formula for dilation:
\[
\text{Radius of original circle} = \frac{\text{Radius of dilated circle}}{\text{Scale factor}}
\]
Given:
- Radius of the dilated circle = 18 cm
- Scale factor = \( \frac{2}{3} \)
Plugging these values into the formula:
\[
\text{Radius of original circle} = \frac{18 \text{ cm}}{\frac{2}{3}} = 18 \text{ cm} \times \frac{3}{2} = 27 \text{ cm}
\]
Therefore, the radius of the original circle is **27 cm**.
\[
\text{Radius of original circle} = \frac{\text{Radius of dilated circle}}{\text{Scale factor}}
\]
Given:
- Radius of the dilated circle = 18 cm
- Scale factor = \( \frac{2}{3} \)
Plugging these values into the formula:
\[
\text{Radius of original circle} = \frac{18 \text{ cm}}{\frac{2}{3}} = 18 \text{ cm} \times \frac{3}{2} = 27 \text{ cm}
\]
Therefore, the radius of the original circle is **27 cm**.