To find the volume of an oblique pyramid with a square base, we can use the formula for the volume of a pyramid, which is given by:
[tex]\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Here's the step-by-step process:
1. Determine the base area:
The pyramid has a square base with edges measuring [tex]\( x \)[/tex] cm. So, the area of the square base ([tex]\( \text{Base Area} \)[/tex]) is:
[tex]\[ \text{Base Area} = x \times x = x^2 \, \text{cm}^2 \][/tex]
2. Determine the height:
The height of the pyramid is given as [tex]\( (x + 2) \)[/tex] cm.
3. Calculate the volume:
We substitute the base area and the height into the volume formula:
[tex]\[ \text{Volume} = \frac{1}{3} \times x^2 \times (x + 2) \][/tex]
4. Simplify the expression inside the parentheses:
First, distribute [tex]\( x^2 \)[/tex] inside the parentheses:
[tex]\[ x^2 \times (x + 2) = x^2 \times x + x^2 \times 2 = x^3 + 2x^2 \][/tex]
5. Include the [tex]\(\frac{1}{3}\)[/tex] factor:
Finally, we multiply by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \text{Volume} = \frac{1}{3} \times (x^3 + 2x^2) \][/tex]
6. Write the final expression:
The volume of the pyramid is:
[tex]\[ \text{Volume} = \frac{x^3 + 2x^2}{3} \, \text{cm}^3 \][/tex]
Thus, the correct expression representing the volume of the pyramid is:
[tex]\(\boxed{\frac{x^3 + 2 x^2}{3} \, \text{cm}^3}\)[/tex]
