Question

If you use a scale factor of 15
to create a circle with radius 18 cm, what is the radius of the original circle you dilated?

Answer 1

To find the radius of the original circle before dilation, you can use the scale factor. The scale factor describes how much the original figure is enlarged or reduced.

Given:
- Scale factor = 15
- New radius (after dilation) = 18 cm

The formula to find the original radius (R) when you know the new radius (r) and the scale factor (k) is:

\[
r = k \times R
\]

You can rearrange this formula to find the original radius:

\[
R = \frac{r}{k}
\]

Substituting the known values:

\[
R = \frac{18 \, \text{cm}}{15}
\]

Calculating:

\[
R = 1.2 \, \text{cm}
\]

So, the radius of the original circle is **1.2 cm**.