If the circumference of circle X is 12π and the circumference of circle Z is 6π, then what is the scale factor from X to Z?(1 point)

Question

Responses

1:2
ratio of 1 to 2

1:3
ratio of 1 to 3

3:1
ratio of 3 to 1

2:1

Answer 1

To find the scale factor from circle X to circle Z based on their circumferences, we can first calculate the radii of both circles using the formula for circumference:

\[ C = 2\pi r \]

For circle X: \[ 12\pi = 2\pi r_X \] \[ r_X = \frac{12\pi}{2\pi} = 6 \]

For circle Z: \[ 6\pi = 2\pi r_Z \] \[ r_Z = \frac{6\pi}{2\pi} = 3 \]

Now we can determine the scale factor from circle X (radius 6) to circle Z (radius 3). The scale factor is the ratio of the radii (or circumferences), which can be calculated as:

\[ \text{Scale Factor} = \frac{r_X}{r_Z} = \frac{6}{3} = 2 \]

Thus, the scale factor from circle X to circle Z is \(2:1\).

So, the correct answer is: 2:1