If the circumference of circle X

Question

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

2:1
ratio of 2 to 1

3:1
ratio of 3 to 1

1:3
ratio of 1 to 3

1:2

Answer 1

To find the scale factor from circle X to circle Z based on their circumferences, we can use the formula for the circumference of a circle, which is \(C = 2\pi r\), where \(r\) is the radius.

Given:

• Circumference of circle X: \(C_X = 12\pi\)
• Circumference of circle Z: \(C_Z = 6\pi\)

The radii of the circles can be calculated as follows:

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

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

Now, to find the scale factor from circle X to circle Z, we can compare their radii:

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

Therefore, the scale factor from circle X to circle Z is:

2:1 (ratio of 2 to 1).