Sure, let's calculate the volume of an oblique square pyramid step-by-step.
1. Understand the formula for the volume of a pyramid:
The volume [tex]\( V \)[/tex] of a pyramid is given by the formula:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
2. Identify the given values:
- The base edge of the square pyramid is [tex]\( x \)[/tex] cm.
- The height of the pyramid is [tex]\( 9 \)[/tex] cm.
3. Calculate the base area:
Since the base is a square, the area of the base ([tex]\( \text{Base Area} \)[/tex]) can be calculated as:
[tex]\[
\text{Base Area} = x^2 \text{ cm}^2
\][/tex]
4. Substitute the known values into the volume formula:
Plugging in the base area and the height into the volume formula, we get:
[tex]\[
V = \frac{1}{3} \times x^2 \times 9
\][/tex]
5. Simplify the expression:
Simplifying the expression:
[tex]\[
V = \frac{1}{3} \times 9 \times x^2
\][/tex]
[tex]\[
V = 3 \times x^2
\][/tex]
6. Write the final volume expression in terms of [tex]\( x \)[/tex]:
The volume of the oblique square pyramid in terms of [tex]\( x \)[/tex] is:
[tex]\[
3x^2 \text{ cm}^3
\][/tex]
Therefore, the correct answer is [tex]\(\boxed{3x^2 \text{ cm}^3}\)[/tex].
