The question asks to calculate the volume of a rectangular box with the given dimensions in meters and then convert the volume into cubic centimeters ($\text{cm}^3$).

The given dimensions of the box are:

• Length = 0.021 m
• Width = 0.034 m
• Height = 0.010 m

Step 1: Calculate the volume in cubic meters ($\text{m}^3$)

The formula for the volume $V$ of a rectangular box is:

$V = \text{Length} \times \text{Width} \times \text{Height}$

Substituting the values:

$V = 0.021 \, \text{m} \times 0.034 \, \text{m} \times 0.010 \, \text{m}$

Let me compute that.The volume of the rectangular box is $7.14 \times 10^{-6}$ cubic meters ($\text{m}^3$).

Step 2: Convert the volume to cubic centimeters ($\text{cm}^3$)

Since $1 \, \text{m}^3 = 1,000,000 \, \text{cm}^3$, we can multiply the result by $10^6$ to convert it to cubic centimeters.

Let me calculate that.The volume of the rectangular box is $7.14 \, \text{cm}^3$.

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. How would the volume change if the dimensions were in centimeters from the start?
2. What is the formula for the volume of other shapes, like cylinders or spheres?
3. How do we convert between other units of volume, such as liters and cubic meters?
4. What happens to the volume if you double each dimension of the box?
5. Can you describe how volume scaling works when you increase one or more dimensions proportionally?

Tip: Always make sure to use consistent units when calculating volume, especially if you're converting to a different unit at the end.