Mid-Chapter Quiz
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Think about the formula for the volume of a rectangular prism.
C
To find the area of the base, we need to consider the formula for volume of a rectangular prism.
V= B * h, where Bis the area of the base
We know that the height h is given as x+3. We are also given that the volume of the rectangular prism V is 6x^3+19x^2+2x-3.
Given our formula for the volume, we know that the product of our height x+3 and the expression for the base should equal our volume of the rectangular prism. Let's multiply our height by each of the possible expressions for the base to check which one works. Let's begin with option A.
Substitute expressions
Distribute (x+3)
Distribute x
Distribute 3
Add terms
Because the product did not equal the volume, we know that option A is incorrect. In a similar way, we can check options B, C, and D.
| Options | B * h | Product | Equal to V? |
|---|---|---|---|
| B | ( 6x^2+x+1)( x+3) | 6x^3+19x^2+4x+3 | No |
| C | ( 6x^2+x-1) ( x+3) | 6x^3+19x^2+2x-3 | Yes |
| D | ( 6x+1) ( x+3) | 6x^2+19x+3 | No |
After multiplying the choices, we can see that the base is equal to the expression in option C.