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The problem describes a circular pipe with a diameter of 200 cm, where a segment of 120 cm has been cut out from the top. We need to find the depth of the ditch (or the remaining part of the pipe) to the nearest tenth of a centimeter.

### Key Information:
- Diameter of the pipe \( D = 200 \, \text{cm} \)
- Radius \( r = \frac{D}{2} = 100 \, \text{cm} \)
- Length of the cut segment \( s = 120 \, \text{cm} \)

The task is to find the remaining depth of the ditch, which corresponds to the vertical distance between the bottom of the pipe and the top edge of the remaining portion (after the cut).

#### Approach:
The cut creates a segment of the circle, leaving us with a chord of length 120 cm at the top. We can use the formula for the sagitta (depth) of a circular segment:

\[
d = r - \sqrt{r^2 - \left(\frac{s}{2}\right)^2}
\]

Where:
- \( d \) is the depth of the ditch
- \( r \) is the radius of the pipe
- \( s \) is the length of the chord (120 cm in this case)

Let's calculate the depth of the ditch using this formula.The depth of the ditch is 20.0 cm to the nearest tenth of a centimeter.

Would you like further details or have any questions? Here are five related questions you can explore:

1. How would the depth change if the pipe's diameter increased to 300 cm?
2. What formula can be used to find the area of the remaining pipe segment?
3. How can the problem be approached if the chord length is unknown, but the angle of the cut is provided?
4. How does the radius affect the sagitta in a circle for a given chord length?
5. What if only half the chord length was cut out — what would the new depth be?

**Tip:** Always check that the segment length (chord) is less than the diameter when using this formula!

An open drainage ditch is made using metal pipes with a diameter of 200 cm. To create an opening on the top of each pipe, workers must cut and remove a section on each pipe as shown. The cut segment length is 120 cm. What is the depth of the ditch, to the nearest tenth of a centimetre?

Solve the problem of finding the depth of a circular segment created by cutting a 120 cm chord from a 200 cm diameter pipe. This problem involves geometric concepts like circle properties and the formula for the depth of a circular segment. Suitable for students in Grades 8-10.

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