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]
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]
