Final answer:
The diameter of the top of the nuclear cooling tower is 902 ft, and the diameter of the base is 1804 ft, as derived from the properties of the hyperbola representing the cross-section of the tower.
Step-by-step explanation:
The cross-section of the nuclear cooling tower is a hyperbola with the equation x²/902 − y²/1302 = 1. According to the problem, the tower is 450 ft tall, and the distance from the top of the tower to the center of the hyperbola is half the distance from the base of the tower to the center. To find the diameters at the top and the base, we need to analyze the properties of the hyperbola.
For the hyperbola equation x²/a² − y²/b² = 1, where a and b are the semi-major and semi-minor axes, the lengths of the axes are twice the values of a and b. Therefore, the diameter of the base, which aligns with the variable x, is twice 902 ft, which equals 1804 ft. The diameter of the top, on the other hand, is half that of the base since at the top we're dealing with the height from the center to the top of the tower.
Hence, the top diameter is 1804 ÷ 2 = 902 ft. So, the answer is Top: 902 ft, Base: 1804 ft.