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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]

Sagot :

GinnyAnswer
Sure! Let's find the volume of the pyramid step-by-step.

Given:
- The base edge of the square pyramid is [tex]\( x \)[/tex] cm.
- The height of the pyramid is [tex]\( 9 \)[/tex] cm.

A square pyramid's volume [tex]\( V \)[/tex] is calculated using the formula for the volume of a pyramid:
[tex]\[ V = \frac{1}{3} \text{ (Base Area) (Height)} \][/tex]

1. Calculate the Base Area:
Since the base of the pyramid is a square, the area of the base (Base Area) is given by:
[tex]\[ \text{Base Area} = x^2 \][/tex]
where [tex]\( x \)[/tex] is the length of each side of the square base.

2. Determine the Volume:
Using the pyramid volume formula:
[tex]\[ V = \frac{1}{3} \text{ (Base Area) (Height)} \][/tex]
Substituting the base area and the height we get:
[tex]\[ V = \frac{1}{3} \text{ } x^2 \text{ } 9 \][/tex]

3. Simplify:
Now, simplify the expression:
[tex]\[ V = \frac{1}{3} \text{ * } 9 x^2 \][/tex]
[tex]\[ V = 3 x^2 \][/tex]

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

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