To determine the volume of a solid oblique pyramid with a square base, we can use the formula for the volume of a pyramid:
[tex]\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Given:
- The edge length of the square base [tex]\( x \, \text{cm} \)[/tex].
- The height of the pyramid [tex]\( (x + 2) \, \text{cm} \)[/tex].
Let's break down the steps to find the volume:
1. Calculate the base area:
Since the base is a square with side length [tex]\( x \, \text{cm} \)[/tex], the area of the base [tex]\( \text{(Base Area)} \)[/tex] is:
[tex]\[
x^2 \, \text{cm}^2
\][/tex]
2. Identify the height:
The height [tex]\( \text{(Height)} \)[/tex] of the pyramid is:
[tex]\[
(x + 2) \, \text{cm}
\][/tex]
3. Substitute into the volume formula:
Plugging the base area and height into the pyramid volume formula gives:
[tex]\[
\text{Volume} = \frac{1}{3} \times x^2 \times (x + 2)
\][/tex]
4. Simplify the expression:
Multiply [tex]\( x^2 \)[/tex] and [tex]\( (x + 2) \)[/tex]:
[tex]\[
x^2 \times (x + 2) = x^3 + 2x^2
\][/tex]
So, substituting back gives:
[tex]\[
\text{Volume} = \frac{1}{3} \times (x^3 + 2x^2)
\][/tex]
Simplifying this fraction:
[tex]\[
\text{Volume} = \frac{x^3 + 2x^2}{3}
\][/tex]
Hence, the correct expression for the volume of the pyramid is:
[tex]\[
\frac{x^3 + 2 x^2}{3} \, \text{cm}^3
\][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{\frac{x^3+2 x^2}{3} \, \text{cm}^3} \][/tex]
