The base edge of an oblique square pyramid is represented as [tex]x \, \text{cm}[/tex]. If the height is [tex]9 \, \text{cm}[/tex], what is the volume of the pyramid in terms of [tex]x[/tex]?

A. [tex]3x^2 \, \text{cm}^3[/tex]
B. [tex]9x^2 \, \text{cm}^3[/tex]
C. [tex]3x \, \text{cm}^3[/tex]
D. [tex]x \, \text{cm}^3[/tex]



Answer :

To solve this problem, let's follow these steps:

1. Understand the formula for the volume of a pyramid:

The formula for the volume of a pyramid is given by:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

2. Identify given values:

- The base of the pyramid is a square with each edge \( x \, \text{cm} \).
- The height of the pyramid is \( 9 \, \text{cm} \).

3. Calculate the base area:

Since the base is a square and the side length is \( x \, \text{cm} \), the area of the base (Base Area) is:
[tex]\[ \text{Base Area} = x^2 \][/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]\[ V = \frac{1}{3} \times 9 \times x^2 = 3 x^2 \][/tex]

Thus, the volume of the pyramid in terms of \( x \) is:
[tex]\[ V = 3x^2 \, \text{cm}^3 \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{3x^2 \, \text{cm}^3} \][/tex]