Answer :
To determine the volume of an oblique prism, you need to use the formula for the volume of any prism, which is given by:
[tex]\[ V = B \cdot h \][/tex]
where:
- \( V \) is the volume of the prism,
- \( B \) is the area of the base of the prism,
- \( h \) is the height of the prism.
In this problem, we are given that the base area \( B = 3x^2 \) square units.
However, we are not provided with a specific height \( h \). Instead, we can infer that one of the multiple-choice options likely represents a volume expression that incorporates a particular height.
Since the base area \( B = 3x^2 \), let's consider each option to determine if it could result from multiplying the base area by a specific height:
1. \( 15x^2 \):
[tex]\[ V = 3x^2 \cdot h \][/tex]
To get \( V = 15x^2 \),
[tex]\[ 3x^2 \cdot h = 15x^2 \][/tex]
[tex]\[ h = 5 \][/tex]
This works as it represents a possible height of 5 units.
2. \( 24x^2 \):
[tex]\[ V = 3x^2 \cdot h \][/tex]
To get \( V = 24x^2 \),
[tex]\[ 3x^2 \cdot h = 24x^2 \][/tex]
[tex]\[ h = 8 \][/tex]
This works as it represents a possible height of 8 units.
3. \( 36x^2 \):
[tex]\[ V = 3x^2 \cdot h \][/tex]
To get \( V = 36x^2 \),
[tex]\[ 3x^2 \cdot h = 36x^2 \][/tex]
[tex]\[ h = 12 \][/tex]
This works as it represents a possible height of 12 units.
4. \( 39x^2 \):
[tex]\[ V = 3x^2 \cdot h \][/tex]
To get \( V = 39x^2 \),
[tex]\[ 3x^2 \cdot h = 39x^2 \][/tex]
[tex]\[ h = 13 \][/tex]
This works as it represents a possible height of 13 units.
Given the choices \( 15x^2 \), \( 24x^2 \), \( 36x^2 \), and \( 39x^2 \), we see that any of these could be a valid volume of the prism with different corresponding heights. Hence, we need clarification from additional context to choose among the provided options.
Since the problem does not specify the exact height \( h \), any calculation assuming a specific height amongst the provided options can be correct.
To summarize, each expression represents the volume of the prism with differing heights. The available options correspond to:
[tex]\[ 15x^2 \text{ cubic units if } h = 5 \][/tex]
[tex]\[ 24x^2 \text{ cubic units if } h = 8 \][/tex]
[tex]\[ 36x^2 \text{ cubic units if } h = 12 \][/tex]
[tex]\[ 39x^2 \text{ cubic units if } h = 13 \][/tex]
Given the choices and without more context, any of these could be perceived as correct depending on the assumed height. Hence it is generally correct to confirm with more problem specifics, not provided here beyond confirming each volume’s potential.
[tex]\[ V = B \cdot h \][/tex]
where:
- \( V \) is the volume of the prism,
- \( B \) is the area of the base of the prism,
- \( h \) is the height of the prism.
In this problem, we are given that the base area \( B = 3x^2 \) square units.
However, we are not provided with a specific height \( h \). Instead, we can infer that one of the multiple-choice options likely represents a volume expression that incorporates a particular height.
Since the base area \( B = 3x^2 \), let's consider each option to determine if it could result from multiplying the base area by a specific height:
1. \( 15x^2 \):
[tex]\[ V = 3x^2 \cdot h \][/tex]
To get \( V = 15x^2 \),
[tex]\[ 3x^2 \cdot h = 15x^2 \][/tex]
[tex]\[ h = 5 \][/tex]
This works as it represents a possible height of 5 units.
2. \( 24x^2 \):
[tex]\[ V = 3x^2 \cdot h \][/tex]
To get \( V = 24x^2 \),
[tex]\[ 3x^2 \cdot h = 24x^2 \][/tex]
[tex]\[ h = 8 \][/tex]
This works as it represents a possible height of 8 units.
3. \( 36x^2 \):
[tex]\[ V = 3x^2 \cdot h \][/tex]
To get \( V = 36x^2 \),
[tex]\[ 3x^2 \cdot h = 36x^2 \][/tex]
[tex]\[ h = 12 \][/tex]
This works as it represents a possible height of 12 units.
4. \( 39x^2 \):
[tex]\[ V = 3x^2 \cdot h \][/tex]
To get \( V = 39x^2 \),
[tex]\[ 3x^2 \cdot h = 39x^2 \][/tex]
[tex]\[ h = 13 \][/tex]
This works as it represents a possible height of 13 units.
Given the choices \( 15x^2 \), \( 24x^2 \), \( 36x^2 \), and \( 39x^2 \), we see that any of these could be a valid volume of the prism with different corresponding heights. Hence, we need clarification from additional context to choose among the provided options.
Since the problem does not specify the exact height \( h \), any calculation assuming a specific height amongst the provided options can be correct.
To summarize, each expression represents the volume of the prism with differing heights. The available options correspond to:
[tex]\[ 15x^2 \text{ cubic units if } h = 5 \][/tex]
[tex]\[ 24x^2 \text{ cubic units if } h = 8 \][/tex]
[tex]\[ 36x^2 \text{ cubic units if } h = 12 \][/tex]
[tex]\[ 39x^2 \text{ cubic units if } h = 13 \][/tex]
Given the choices and without more context, any of these could be perceived as correct depending on the assumed height. Hence it is generally correct to confirm with more problem specifics, not provided here beyond confirming each volume’s potential.
