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Let's go through each part of the question:

### Part (a): Find the depth of water when the following amounts of water are poured in.
You are given:
- Container dimensions: 10 cm long, 5 cm wide, and 8 cm high.
- Volumes of water to be poured: 
  - (i) 400 mL
  - (ii) 200 mL
  - (iii) 160 mL
  
Since \(1 \, \text{mL} = 1 \, \text{cm}^3\), we will treat the volumes of water as cubic centimeters.

**Formula**:
\[
\text{Volume} = \text{Base Area} \times \text{Depth}
\]
\[
\text{Depth} = \frac{\text{Volume}}{\text{Base Area}}
\]

The base area of the container:
\[
\text{Base Area} = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]

Now calculate the depth for each case:

1. **For 400 mL**:
   \[
   \text{Depth} = \frac{400 \, \text{cm}^3}{50 \, \text{cm}^2} = 8 \, \text{cm}
   \]

2. **For 200 mL**:
   \[
   \text{Depth} = \frac{200 \, \text{cm}^3}{50 \, \text{cm}^2} = 4 \, \text{cm}
   \]

3. **For 160 mL**:
   \[
   \text{Depth} = \frac{160 \, \text{cm}^3}{50 \, \text{cm}^2} = 3.2 \, \text{cm}
   \]

### Part (b): After adding 200 mL, a further 30 mL is added. What is the increase in depth?
- Initial volume: 200 mL (already poured in).
- Additional volume: 30 mL.

The total volume of water:
\[
\text{Total Volume} = 200 \, \text{cm}^3 + 30 \, \text{cm}^3 = 230 \, \text{cm}^3
\]

Calculate the new depth after adding the 30 mL:
\[
\text{New Depth} = \frac{230 \, \text{cm}^3}{50 \, \text{cm}^2} = 4.6 \, \text{cm}
\]

Now, the increase in depth:
\[
\text{Increase in Depth} = 4.6 \, \text{cm} - 4 \, \text{cm} = 0.6 \, \text{cm}
\]

### Part (c): A 1-liter container of milk has a base area of 8 cm by 7 cm. After 250 mL of milk is poured out, what is the depth of the remaining milk?
- 1 liter = 1000 mL, and 250 mL is poured out, so:
\[
\text{Remaining Volume} = 1000 \, \text{mL} - 250 \, \text{mL} = 750 \, \text{mL}
\]
The base area of the container:
\[
\text{Base Area} = 8 \, \text{cm} \times 7 \, \text{cm} = 56 \, \text{cm}^2
\]

Now calculate the depth of the remaining milk:
\[
\text{Depth} = \frac{750 \, \text{cm}^3}{56 \, \text{cm}^2} \approx 13.39 \, \text{cm}
\]

To the nearest millimeter, the depth is approximately **13.4 cm**.

---

Let me know if you need more details or clarifications! Here are five related questions you might find helpful:

1. How would the depth change if the dimensions of the container were different?
2. What is the total capacity of the container if it's filled to the top?
3. How would the depth change if we added another 50 mL of water?
4. How does the base area affect the depth for a given volume?
5. How can you calculate the volume if only the depth is known?

**Tip:** Always check units carefully, especially when converting between milliliters and cubic centimeters.

A container is 10 cm long, 5 cm wide, and 8 cm high. Find the depth of water when different amounts of water are poured in. Calculate increase in depth after adding more water, and find the depth of milk in a different container after a certain amount is poured out.

Learn how to calculate the depth of water in a container based on different volumes poured in. The solution covers concepts like volume and area. Also, find out how the depth changes after adding more liquid. Suitable for students in Grades 6-8.

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