Answer:
C. [tex]x^2*(x-2)\text{ Cubic units}[/tex]
Step-by-step explanation:
We have been given a diagram of an oblique prism and we are asked to choose the expression that represents the volume of the prism.
Since we know that an oblique prism is a prism in which the bases are parallel, but the faces are not directly one over the other.
The volume of an oblique prism is base area multiplied by the height.
[tex]\text{Volume of an oblique prism}=\text{Base area* Height of the prism}[/tex]
We can see from our diagram that our prism has an square base as each side of base equals x units.
[tex]\text{Base area of prism}=x\text{ units}*x\text{ units}[/tex]
[tex]\text{Base area of prism}=x^2\text{ units}^2[/tex]
We can also see from our given diagram that it has a height of (x-2) units and slant height of (x+1) units.
Since volume of oblique prism is base area times by the height (not slant height). So upon substituting the height and base area of our given prism in volume formula we will get,
[tex]\text{Volume of an oblique prism}=x^2\text{ units}^2*(x-2)\text{ units}[/tex]
[tex]\text{Volume of an oblique prism}=x^2*(x-2)\text{ units}^3[/tex]
Therefore, the volume of our given prism is [tex]x^2*(x-2)\text{ Cubic units}[/tex] and option C is the correct choice.
