To determine the volume of the right rectangular prism whose height is 3 units greater than the side length of its square base, we need to follow these steps:
1. Understand the dimensions of the prism:
- The length of the base is [tex]\( x \)[/tex] units.
- The width of the base is also [tex]\( x \)[/tex] units, since it is a square base.
- The height of the prism is [tex]\( x + 3 \)[/tex] units because it is given that the height is 3 units greater than the length of the base.
2. Write the formula for the volume of a right rectangular prism:
The volume [tex]\( V \)[/tex] of a right rectangular prism can be calculated using the formula:
[tex]\[
V = \text{base\_area} \times \text{height}
\][/tex]
3. Calculate the base area:
The base is a square with each side of length [tex]\( x \)[/tex] units.
[tex]\[
\text{base\_area} = x \times x = x^2
\][/tex]
4. Calculate the volume:
Using the base area and the height, the volume of the prism can be calculated as:
[tex]\[
V = \text{base\_area} \times \text{height} = x^2 \times (x + 3)
\][/tex]
5. Simplify the expression:
We need to expand the expression [tex]\( x^2 \times (x + 3) \)[/tex]:
[tex]\[
x^2 \times (x + 3) = x^2 \times x + x^2 \times 3 = x^3 + 3x^2
\][/tex]
So, the expression that represents the volume of the prism, in cubic units, is [tex]\( x^3 + 3x^2 \)[/tex].
Therefore, the correct answer is:
[tex]\[
x^3 + 3x^2
\][/tex]
