The base of a rectangular box is 6 centimeter by 40 centimeter. How many measures deep is the box, if it holds one k g of water, show your work.

To determine how deep the box is if it holds 1 kg of water, we can follow these steps:

### Step 1: Determine the volume of the box needed to hold 1 kg of water.
- Water has a density of \(1 \, \text{g/cm}^3\), so 1 kg of water is equivalent to 1000 grams.
- Since the density is \(1 \, \text{g/cm}^3\), 1000 grams of water will occupy \(1000 \, \text{cm}^3\) of volume.

### Step 2: Find the area of the base of the box.
- The base of the rectangular box is \(6 \, \text{cm} \times 40 \, \text{cm}\).
- Area of the base, \( A \), is:
\[
A = 6 \times 40 = 240 \, \text{cm}^2
\]

### Step 3: Calculate the depth of the box.
- Let the depth of the box be \( h \) cm.
- The volume \( V \) of the box can be calculated as:
\[
V = \text{Area of the base} \times \text{Depth}
\]
- We already know the volume is \(1000 \, \text{cm}^3\):
\[
1000 = 240 \times h
\]
- Solve for \( h \):
\[
h = \frac{1000}{240} \approx 4.17 \, \text{cm}
\]

### Final Answer:
The box must be approximately **4.17 cm deep** to hold 1 kg of water.

Would you like to explore more details or have any questions?

### Follow-up Questions:
1. How would the depth change if the box's base area were larger?
2. What if the box held a different liquid with a different density?
3. How would you convert the depth from centimeters to millimeters?
4. What is the significance of understanding the density of a liquid when calculating volume?
5. How does the shape of the box affect the required depth for holding a specific volume?

### Tip:
Always remember that the density of water is \(1 \, \text{g/cm}^3\), which simplifies many volume-related calculations.

Learn how to calculate the depth of a rectangular box to hold 1 kg of water. This problem involves geometry, volume calculation based on the box's base area, and understanding the density of water. Suitable for Grades 7-9.

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