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Writing an Algebraic Expression for Volume

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

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



Answer :

GinnyAnswer
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]

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