Let's determine the volume of a right pyramid with a square base step-by-step.
1. Identify the given dimensions:
- The length of each side of the square base is [tex]\( x \)[/tex] inches.
- The height of the pyramid is [tex]\( 2 \)[/tex] inches longer than the base side length, which means the height is [tex]\( x + 2 \)[/tex] inches.
2. Determine the area of the square base:
The area of the base (which is a square) can be calculated using the formula for the area of a square:
[tex]\[
\text{Base Area} = x^2
\][/tex]
3. Recall the volume formula for a pyramid:
The volume [tex]\( V \)[/tex] of a pyramid with a square base is calculated using the formula:
[tex]\[
V = \frac{\text{Base Area} \times \text{Height}}{3}
\][/tex]
4. Substitute the given dimensions into the formula:
- The base area is [tex]\( x^2 \)[/tex].
- The height is [tex]\( x + 2 \)[/tex].
So, substituting these values in, we get:
[tex]\[
V = \frac{x^2 \times (x + 2)}{3}
\][/tex]
5. Simplify the expression:
The expression for the volume simplifies to:
[tex]\[
V = \frac{x^2 (x + 2)}{3}
\][/tex]
Therefore, the correct expression that represents the volume of the right pyramid in terms of [tex]\( x \)[/tex] is:
[tex]\[
\boxed{\frac{x^2 (x + 2)}{3} \text{ cubic inches}}
\][/tex]
