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Let's solve each part of this problem step by step.

### Part (a): Finding the depth of water for given amounts of water.
The container has dimensions:
- Length = 10 cm
- Width = 5 cm
- Height = 8 cm

The formula for the volume of a rectangular container is:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Depth}
\]

Here, 1 mL = 1 cm³. So, we can find the depth for each volume by rearranging the formula to:

\[
\text{Depth} = \frac{\text{Volume}}{\text{Length} \times \text{Width}} = \frac{\text{Volume}}{10 \times 5}
\]

Thus, the depth for different volumes can be calculated as follows:

#### i. For 400 mL:
\[
\text{Depth} = \frac{400}{10 \times 5} = \frac{400}{50} = 8 \text{ cm}
\]

#### ii. For 200 mL:
\[
\text{Depth} = \frac{200}{10 \times 5} = \frac{200}{50} = 4 \text{ cm}
\]

#### iii. For 160 mL:
\[
\text{Depth} = \frac{160}{10 \times 5} = \frac{160}{50} = 3.2 \text{ cm}
\]

### Part (b): After adding 200 mL, a further 30 mL is added. What is the increase in depth?
The total volume added is 200 mL + 30 mL = 230 mL.

The depth corresponding to 230 mL is:

\[
\text{Depth} = \frac{230}{10 \times 5} = \frac{230}{50} = 4.6 \text{ cm}
\]

Now, the increase in depth from adding just the 30 mL is the difference between the depth for 230 mL and 200 mL:
\[
\text{Increase in depth} = 4.6 \text{ cm} - 4 \text{ cm} = 0.6 \text{ cm}
\]

### Part (c): Milk container problem.
Here, the base area is given as:
- Length = 8 cm
- Width = 7 cm

The total volume of the container is 1 L = 1000 mL.

After pouring out 250 mL, the remaining volume is:
\[
1000 \, \text{mL} - 250 \, \text{mL} = 750 \, \text{mL}
\]

The depth of the remaining milk is:

\[
\text{Depth} = \frac{750}{8 \times 7} = \frac{750}{56} \approx 13.39 \, \text{cm}
\]

Rounded to the nearest mm:
\[
\text{Depth} \approx 13.4 \, \text{cm}
\]

---

Would you like any further explanation on these solutions? 

Here are 5 related questions to practice:
1. What is the depth of water in the same container for 500 mL of water?
2. How much volume would be required to fill the container to a depth of 6 cm?
3. If you have 700 mL of water, what will be the depth in a container with dimensions 8 cm × 6 cm?
4. What is the volume of a container with dimensions 12 cm × 5 cm × 8 cm?
5. How much milk needs to be poured out to leave a depth of 5 cm in the milk container from part (c)?

**Tip**: Always double-check unit conversions when working with volume, especially when switching between milliliters and cubic centimeters!

A container is 10 cm long, 5 cm wide, and 8 cm high. Find the depth of water when 400 mL, 200 mL, and 160 mL of water are poured in. After adding 200 mL, a further 30 mL is added. What is the increase in depth? A 1-litre 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 milk remaining in the container? Give your answer to the nearest mm.

Solve problems related to depth calculation in containers with given volumes of water and milk. Learn step-by-step how to calculate the depth when different volumes of liquid are poured into a container, suitable for students in Grades 6-8.

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