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Write an algebraic expression for the volume of an oblique square pyramid.

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

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



Answer :

GinnyAnswer
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].

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