To find the volume of an oblique square pyramid with a base edge represented as [tex]\( x \, \text{cm} \)[/tex] and a height of [tex]\( 9 \, \text{cm} \)[/tex], we use the formula for the volume of a pyramid:
[tex]\[
V = \frac{1}{3} \times \text{base area} \times \text{height}
\][/tex]
First, let's determine the base area:
- Since the base is a square with edge length [tex]\( x \, \text{cm} \)[/tex], the area of the base ([tex]\( \text{base area} \)[/tex]) is given by:
[tex]\[
\text{base area} = x^2
\][/tex]
Next, the volume of the pyramid is calculated as follows:
- Substitute the base area ([tex]\( x^2 \)[/tex]) and the height ([tex]\( 9 \, \text{cm} \)[/tex]) into the volume formula:
[tex]\[
V = \frac{1}{3} \times x^2 \times 9
\][/tex]
- Simplify this expression:
[tex]\[
V = \frac{1}{3} \times 9 \times x^2 = 3 x^2
\][/tex]
So, the volume of the pyramid in terms of [tex]\( x \)[/tex] is:
[tex]\[
3 x^2 \, \text{cm}^3
\][/tex]
Therefore, the correct answer is:
[tex]\[
3 x^2 \, \text{cm}^3
\][/tex]
