Final answer:
The problem requires finding the dimensions of a fuel tank by solving a polynomial equation that represents the volume. Upon checking the given answer choices with the volume equation, none of the options match the given volume of 33,488 cubic feet, suggesting a possible error in the question or choices.
Step-by-step explanation:
To find the dimensions of the fuel tank, we can use the given information to set up an equation. Let's call the width of the tank w feet. Then, the length would be w + 5 feet and the depth would be w + 29 feet.
The volume of a rectangular prism is calculated by multiplying its length, width, and depth. So, the equation for the volume would be:
V = w × (w + 5) × (w + 29).
We're given that the volume V is 33,488 cubic feet. To find w, we need to solve the following polynomial equation:
33,488 = w^3 + 34w^2 + 145w.
Using synthetic division or other polynomial solving techniques will give us the potential roots, but based on the choices provided in the question, we can test which width will give us the correct volume. The correct dimensions will satisfy our original equation.
Now let's test the answers:
- For choice A, the width should be 10 feet. Plugging it in the equation: 10 × 15 × 39 = 5,850, which is not equal to 33,488.
- For choice B, with width 8 feet: 8 × 13 × 37 = 3,864, which is also incorrect.
- For choice C, with width 1 foot: 1 × 6 × 30 = 180, which is far less than 33,488.
- For choice D, with width 0.5 feet: 0.5 × 5.5 × 29.5 ≤ 80.375, again, incorrect.
It seems that none of the options provided actually result in the volume stated, which implies there might be a typographical error either in the question or the answer choices. Therefore, we cannot determine the answer based on the provided solutions.