To find the volume of a solid right pyramid with a square base, we can use the formula for the volume of a pyramid:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
### Step-by-Step Solution
1. Identify the base area:
The base of the pyramid is a square. Let the edge length of the square base be [tex]\( n \)[/tex] units. The area of the square base is given by:
[tex]\[ \text{Base Area} = n \times n = n^2 \][/tex]
2. Identify the height of the pyramid:
According to the problem, the height of the pyramid is [tex]\( n - 1 \)[/tex] units.
3. Apply the volume formula:
Plug the base area and height into the volume formula for a pyramid:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Substituting the values for the base area and height, we get:
[tex]\[ V = \frac{1}{3} \times n^2 \times (n - 1) \][/tex]
4. Simplify the expression:
The simplified expression for the volume of the pyramid is:
[tex]\[ V = \frac{1}{3} n^2 (n - 1) \][/tex]
### Conclusion
The expression that represents the volume of the pyramid is:
[tex]\[ \frac{1}{3} n^2 (n - 1) \text{ units}^3 \][/tex]
So, the correct choice from the given options is:
[tex]\[ \boxed{\frac{1}{3} n^2 (n - 1) \text{ units}^3} \][/tex]
