Question

page 7 of 7 Similar Circles Quick Check 4 of 54 of 5 Items Question 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) Responses 1:2 ratio of 1 to 2 3:1 ratio of 3 to 1 1:3 ratio of 1 to 3 2:1 ratio of 2 to 1 Skip to navigation

Answer 1

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

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

First, we can determine the radii of both circles.

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

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, we can find the scale factor by taking the ratio of the radii:
\[
\text{Scale factor from X to Z} = \frac{r_Z}{r_X} = \frac{3}{6} = \frac{1}{2}
\]

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

Therefore, the correct response is:
**1:2 (ratio of 1 to 2)**.