To calculate the volume of the pyramid, we use the formula:

$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$

Step 1: Calculate the base area

The base of this pyramid is a square with side length $20 \, \text{mm}$. The area of the base is:

$\text{Base Area} = \text{side}^2 = 20^2 = 400 \, \text{mm}^2$

Step 2: Use the height

The height of the pyramid is given as $15 \, \text{mm}$.

Step 3: Calculate the volume

Substitute the values into the formula:

$V = \frac{1}{3} \times 400 \times 15 = \frac{1}{3} \times 6000 = 2000 \, \text{mm}^3$

Final Answer:

The volume of the pyramid is:

$\boxed{2000 \, \text{mm}^3}$

Would you like further details or an explanation of the steps? Here are some related questions you might explore:

1. What is the significance of the height in the volume calculation?
2. How does the formula for the volume of a pyramid differ from that of a prism?
3. What happens if the base is a rectangle instead of a square?
4. How can we calculate the slant height of this pyramid?
5. What units should be used when working with different dimensions in the formula?

Tip: Always ensure the base dimensions and height are perpendicular for accurate volume calculation!