https://file.aiquickdraw.com/mathbot/file/1726318395497fkryepf8.jpg

The problem you've uploaded involves a circle with center \( W \) and radius \( r \). The angle subtended by arc \( XYZ \) is \( 70^\circ \), and you are asked to find the length of arc \( XYZ \) in terms of \( r \).

### Solution:

The length \( L \) of an arc is given by the formula:

\[
L = \frac{\theta}{360^\circ} \times 2\pi r
\]

Where:
- \( \theta \) is the central angle in degrees (here \( 70^\circ \)).
- \( r \) is the radius of the circle.
- \( 2\pi r \) is the circumference of the circle.

Substituting the given values:

\[
L = \frac{70^\circ}{360^\circ} \times 2\pi r
\]

Simplifying:

\[
L = \frac{7}{36} \times 2\pi r = \frac{7\pi r}{18}
\]

Thus, the length of the arc \( XYZ \) is \( \frac{7\pi r}{18} \).

### Correct Answer:
(A) \( \frac{7\pi r}{18} \)

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Would you like further details on any part of this solution? 

Here are 5 related questions you might find helpful:
1. How do you calculate the length of an arc if the angle is in radians?
2. What is the formula for the area of a sector of a circle?
3. How can the length of an arc be expressed if the central angle is given in radians?
4. How does the arc length change if the radius doubles while keeping the angle constant?
5. What is the relationship between arc length and the total circumference of a circle?

**Tip:** Always ensure that the angle used in arc length calculations is in degrees or radians, consistent with the formula you are using.

The circle above has a center at W and a radius of r. The measure of angle XWZ is 70°. What is the length of arc XYZ in terms of r?

Learn how to calculate the length of arc XYZ in a circle with center W, radius r, and a central angle of 70°. This solution uses the arc length formula L = (θ/360) × 2πr and is suitable for students in Grades 9-11.

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