Sure! Let's go through the solution step-by-step to find the volume of an oblique square pyramid in terms of [tex]\( x \)[/tex].
### Step-by-Step Solution
1. Identify the Variables:
- The base edge of the square pyramid is given by [tex]\( x \)[/tex] cm.
- The height of the pyramid is given as 9 cm.
2. Recall the Formula for the Volume of a Square Pyramid:
The volume [tex]\( V \)[/tex] of a square pyramid can be calculated using the formula:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
3. Calculate the Base Area:
Since the base is a square with side length [tex]\( x \)[/tex], the area of the base [tex]\( A \)[/tex] is:
[tex]\[
A = x^2
\][/tex]
4. Substitute the Base Area and Height into the Volume Formula:
[tex]\[
V = \frac{1}{3} \times x^2 \times 9
\][/tex]
5. Simplify the Expression:
[tex]\[
V = \frac{1}{3} \times 9 \times x^2
\][/tex]
[tex]\[
V = 3 \times x^2
\][/tex]
Therefore, the volume of the oblique square pyramid, in terms of [tex]\( x \)[/tex], is given by:
[tex]\[
3x^2 \, \text{cm}^3
\][/tex]
So the correct answer is:
[tex]\[
3x^2 \, \text{cm}^3
\][/tex]
