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

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



Answer :

GinnyAnswer
To find the volume of an oblique square pyramid given its base edge and height, we follow the formula for the volume of a pyramid:

[tex]\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \][/tex]

1. Determine the base area:
- The base of the pyramid is a square with side length [tex]\( x \)[/tex] cm.
- Therefore, the area of the base is:
[tex]\[ \text{base area} = x^2 \text{ cm}^2 \][/tex]

2. Given the height:
- The height of the pyramid is provided as [tex]\( 9 \)[/tex] cm.

3. Apply the volume formula:
- Substituting the base area and height into the volume formula:
[tex]\[ V = \frac{1}{3} \times (x^2) \times 9 \][/tex]

4. Simplify the expression:
- First, multiply the base area by the height:
[tex]\[ V = \frac{1}{3} \times 9x^2 \][/tex]
- Then, simplify the multiplication by dividing [tex]\( 9x^2 \)[/tex] by 3:
[tex]\[ V = 3x^2 \text{ cm}^3 \][/tex]

Therefore, the volume of the oblique square pyramid in terms of [tex]\( x \)[/tex] is:

[tex]\[ \boxed{3 x^2 \text{ cm}^3} \][/tex]

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