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Let's go through the math problems shown in the image one by one.

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### 17. A container is 10 cm long, 5 cm wide, and 8 cm high.

#### a) Find the depth of water when the following amounts of water are poured in. (Remember: 1 mL = 1 cm³)
To find the depth, we first calculate the volume of the container and then figure out how much water corresponds to the given depths.

The base area of the container is:
\[
\text{Base Area} = \text{Length} \times \text{Width} = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]
Now, for each volume, we can calculate the depth using the formula:
\[
\text{Depth} = \frac{\text{Volume of Water}}{\text{Base Area}}
\]

- **i) 400 mL:**
\[
\text{Depth} = \frac{400 \, \text{cm}^3}{50 \, \text{cm}^2} = 8 \, \text{cm}
\]

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

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

#### b) After adding 200 mL, a further 30 mL is added. What is the increase in depth?

- First, calculate the depth corresponding to 30 mL:
\[
\text{Increase in Depth} = \frac{30 \, \text{cm}^3}{50 \, \text{cm}^2} = 0.6 \, \text{cm}
\]
So, the increase in depth is **0.6 cm**.

#### c) 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?

First, we calculate the base area of the new container:
\[
\text{Base Area} = 8 \, \text{cm} \times 7 \, \text{cm} = 56 \, \text{cm}^2
\]

Next, since 250 mL is poured out from 1 litre (1000 mL), the remaining volume is:
\[
\text{Remaining Volume} = 1000 \, \text{mL} - 250 \, \text{mL} = 750 \, \text{mL}
\]

Now, calculate the depth of the remaining milk:
\[
\text{Depth} = \frac{750 \, \text{cm}^3}{56 \, \text{cm}^2} \approx 13.39 \, \text{cm} \approx 13.4 \, \text{cm}
\]
Rounding to the nearest mm, the depth of milk is **13.4 cm** or **134 mm**.

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Would you like more details or have any questions about these steps?

### Relative questions:
1. How would you calculate the total capacity of a container?
2. How does the base area affect the depth when the same volume is added to different containers?
3. If you had 500 mL of water in the container, what would the depth be?
4. How can you calculate the depth when the base area is unknown but the volume and height are given?
5. What happens to the depth if the same amount of water is poured into a container with double the base area?

### Tip:
Always check units carefully in volume and area problems to avoid mistakes in calculations.

A container is 10 cm long, 5 cm wide, and 8 cm high. a) Find the depth of water when the following amounts of water are poured in: i) 400 mL, ii) 200 mL, iii) 160 mL. b) After adding 200 mL, a further 30 mL is added. What is the increase in depth? c) 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.

Learn how to calculate the depth of water or milk in a container using base area and volume concepts. This includes step-by-step solutions for a 10 cm x 5 cm container and a 1-litre container of milk, along with practical examples of 200 mL, 400 mL, and 160 mL measurements.

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