To determine the volume of an oblique prism, we need to use the formula for the volume of a prism, which is:
[tex]\[ \text{Volume} = \text{Base Area} \times \text{Height} \][/tex]
Given that the base area is [tex]\(3 x^2\)[/tex] square units, let's examine some possible heights that could fit the provided options for the volume.
First, let's consider the scenario for each given volume option:
1. [tex]\(15 x^2\)[/tex]:
[tex]\[ \text{Base Area} = 3 x^2 \][/tex]
Assume the height [tex]\(h = 5\)[/tex]. Substituting in:
[tex]\[ \text{Volume} = (3 x^2) \times 5 = 15 x^2 \][/tex]
2. [tex]\(24 x^2\)[/tex]:
[tex]\[ \text{Base Area} = 3 x^2 \][/tex]
Assume the height [tex]\(h = 8\)[/tex]. Substituting in:
[tex]\[ \text{Volume} = (3 x^2) \times 8 = 24 x^2 \][/tex]
3. [tex]\(36 x^2\)[/tex]:
[tex]\[ \text{Base Area} = 3 x^2 \][/tex]
Assume the height [tex]\(h = 12\)[/tex]. Substituting in:
[tex]\[ \text{Volume} = (3 x^2) \times 12 = 36 x^2 \][/tex]
4. [tex]\(39 x^2\)[/tex]:
[tex]\[ \text{Base Area} = 3 x^2 \][/tex]
Assume the height [tex]\(h = 13\)[/tex]. Substituting in:
[tex]\[ \text{Volume} = (3 x^2) \times 13 = 39 x^2 \][/tex]
From these calculations, we can see that the given expression represents the volume of the prism in cubic units are:
- [tex]\( 15 x^2 \)[/tex]
- [tex]\( 24 x^2 \)[/tex]
- [tex]\( 36 x^2 \)[/tex]
- [tex]\( 39 x^2 \)[/tex]
So, the possible expressions for the volume of the prism, based on the provided information, are as follows:
- [tex]\(15 x^2\)[/tex]
- [tex]\(24 x^2\)[/tex]
- [tex]\(36 x^2\)[/tex]
- [tex]\(39 x^2\)[/tex]
Hence, the expression that correctly represents the volume of the prism is indeed one of these options.
