To solve this problem, we'll calculate the volume of the rectangular box and use the density of water to determine how much volume 1 kg of water occupies.

Step 1: Understanding the Problem

We know the following:

• The dimensions of the rectangular box: 36 cm by 40 cm.
• The mass of water the box holds: 1 kg.

Step 2: Calculating the Volume of Water

Since the density of water is 1 g/cm³ (or equivalently 1 kg/L), 1 kg of water occupies a volume of 1 liter, which is 1000 cm³.

Step 3: Determining the Height of the Box

Let the height of the box be $h$ cm.

The volume $V$ of the rectangular box can be calculated using the formula: $V = \text{length} \times \text{width} \times \text{height}$ Given that the box holds 1 kg of water, the volume $V$ is equal to 1000 cm³.

So, the equation becomes: $36 \times 40 \times h = 1000$

Step 4: Solving for Height

$1440 \times h = 1000$ $h = \frac{1000}{1440} \approx 0.694 \text{ cm}$

Step 5: Final Answer

The height of the box is approximately 0.694 cm.

Would you like more details or have any questions? Here are some related questions:

1. What is the significance of the density of water in this problem?
2. How would the solution change if the box were to hold 2 kg of water?
3. Can you calculate the surface area of the box?
4. What if the box dimensions were in different units?
5. How would you find the height if the box were cylindrical?

Tip: When working with units, always ensure consistency to avoid errors in calculations.