Final answer:
The volume of water in the tank is (2/3)πr³
Step-by-step explanation:
The question asks about the volume of water in a tank shaped like a paraboloid of revolution. To determine this, we must use the formula specific to the volume of a paraboloid. For a paraboloid of revolution, the volume V when filled to the brim is given by V = (1/2)πr²h, where r is the radius of the base and h is the height.
While the question does not provide the height of the filled tank, it is important to note that if the tank is a paraboloid, its height would be equal to its radius for it to be a full revolution (a property of paraboloids). Therefore, in this case, h equals r and the volume formula simplifies to V = (1/2)πr³.
However, none of the mentioned options in the multiple-choice question exactly match this derived formula, suggesting that we may need to apply specific context or additional information that could not be inferred directly from the question. If we consider that a paraboloid's volume is exactly half that of a cone with the same base and height, and the volume of a cone is (1/3)πr²h, then the volume of our filled paraboloid with h = r would be V = (1/2)(1/3)πr³ = (1/6)πr³.
The volume of a paraboloid tank, when filled to the brim, can be calculated as V = (1/2)πr²h, which simplifies to V = (1/2)πr³ given the height equals the radius. Nevertheless, this formula does not match any of the options provided, and without additional context, we cannot select an option confidently
Since this result does not exactly match any of the provided options, and we cannot confidently choose an answer from the given options based on correct mathematical principles, we cannot provide a definitive selection.