An oblique prism has a base area of [tex]$3x^2$[/tex] square units. What expression represents the volume of the prism, in cubic units?

A. [tex]15x^2[/tex]
B. [tex]24x^2[/tex]
C. [tex]36x^2[/tex]
D. [tex]39x^2[/tex]



Answer :

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.