Answer :
To find the volume of a square prism, we need to understand the structure of the prism. A square prism, also known as a rectangular prism or cuboid with a square base, has a base that is a square and a certain height.
Here's how you can calculate the volume step-by-step:
1. Identify the Length of Each Side of the Base:
The problem states that each side of the base of the prism measures [tex]\( 3x \)[/tex].
2. Calculate the Area of the Base:
Since the base is a square, its area can be determined using the formula for the area of a square, which is:
[tex]\[
\text{Area of base} = (\text{side length})^2 = (3x)^2 = 9x^2
\][/tex]
3. Determine the Height of the Prism:
It is given that the height of the prism is [tex]\( 6x \)[/tex].
4. Use the Formula for the Volume of a Prism:
The volume [tex]\( V \)[/tex] of a prism is the product of the area of the base and the height:
[tex]\[
V = \text{Area of base} \times \text{Height}
\][/tex]
Substituting the determined values:
[tex]\[
V = 9x^2 \times 6x
\][/tex]
5. Calculate the Volume:
To calculate [tex]\( 9x^2 \times 6x \)[/tex], you multiply the coefficients and then apply the rule of exponents. This results in:
[tex]\[
V = 54x^3
\][/tex]
Therefore, the volume of the square prism is [tex]\( 54x^3 \)[/tex]. The correct option for the answer is C) 54 x³.
Here's how you can calculate the volume step-by-step:
1. Identify the Length of Each Side of the Base:
The problem states that each side of the base of the prism measures [tex]\( 3x \)[/tex].
2. Calculate the Area of the Base:
Since the base is a square, its area can be determined using the formula for the area of a square, which is:
[tex]\[
\text{Area of base} = (\text{side length})^2 = (3x)^2 = 9x^2
\][/tex]
3. Determine the Height of the Prism:
It is given that the height of the prism is [tex]\( 6x \)[/tex].
4. Use the Formula for the Volume of a Prism:
The volume [tex]\( V \)[/tex] of a prism is the product of the area of the base and the height:
[tex]\[
V = \text{Area of base} \times \text{Height}
\][/tex]
Substituting the determined values:
[tex]\[
V = 9x^2 \times 6x
\][/tex]
5. Calculate the Volume:
To calculate [tex]\( 9x^2 \times 6x \)[/tex], you multiply the coefficients and then apply the rule of exponents. This results in:
[tex]\[
V = 54x^3
\][/tex]
Therefore, the volume of the square prism is [tex]\( 54x^3 \)[/tex]. The correct option for the answer is C) 54 x³.
