The problem asks for the volume of a rectangular pyramid. The formula for the volume of a pyramid is:

$V = \frac{1}{3} \cdot B \cdot h$

Where:

• $B$ is the area of the base.
• $h$ is the height of the pyramid.

From the image:

• The base dimensions are $9 \, \text{in} \times 7 \, \text{in}$, so: $B = 9 \cdot 7 = 63 \, \text{in}^2$

• The height ($h$) of the pyramid is $8 \, \text{in}$.

Substituting these values into the volume formula: $V = \frac{1}{3} \cdot 63 \cdot 8 = \frac{1}{3} \cdot 504 = 168 \, \text{in}^3$

Thus, the volume of the pyramid is:

$\boxed{168 \, \text{in}^3}$

Let me know if you want further clarification or details! Here are related questions to deepen understanding:

1. What is the significance of the $\frac{1}{3}$ factor in the pyramid volume formula?
2. How would the formula change if the pyramid were not rectangular?
3. What units are used for volume, and how do they differ from those used for area?
4. How could we calculate the surface area of the pyramid in this problem?
5. What are other real-world examples of objects with pyramid shapes?

Tip: Always ensure the height you use in the volume formula is perpendicular to the base!