Question

. Used a Scale factor of 2/3 to dilate a circle with radius of 18cm. What is radius or original circle?

Answer 1

To find the radius of the original circle before the dilation, you can use the scale factor of the dilation. The radius of the dilated circle is given by multiplying the original radius by the scale factor.

Let:
- \( r \) = original radius
- Dilation scale factor = \( \frac{2}{3} \)
- Radius of the dilated circle = 18 cm

The relationship can be expressed as:

\[
\text{Radius of dilated circle} = \text{Scale factor} \times \text{Original radius}
\]

This can be rearranged to solve for the original radius:

\[
\text{Original radius} = \frac{\text{Radius of dilated circle}}{\text{Scale factor}}
\]

Substituting the values:

\[
r = \frac{18 \, \text{cm}}{\frac{2}{3}}
\]

Calculating this gives:

\[
r = 18 \, \text{cm} \times \frac{3}{2} = 18 \, \text{cm} \times 1.5 = 27 \, \text{cm}
\]

Thus, the radius of the original circle is **27 cm**.