Final answer:
To calculate the height of a hyperbolic cooling tower given certain dimensions at different heights, additional information is required such as the equation defining the hyperbola. With the provided measurements alone, it is not possible to determine the height of the tower.
Step-by-step explanation:
The question pertains to finding the height of a hyperbolic cooling tower given its dimensions at various points. We know that the width of the tower is 450 feet at the base, 280 feet at the top, and 220 feet at its narrowest point, which is 330 feet above the ground. Unfortunately, without additional information about the specific shape of the hyperbola (such as its equation or additional measurements), we cannot determine the height of the cooling tower using only the provided information.
Normally, one would need to use the equation of a hyperbola to find the relationship between the width of the tower and the height. From there, you could use calculus or algebra (depending on the complexity of the equation) to find the height of the tower based on the given dimensions at specific points.
Since additional information would be required to perform the calculation, such as the exact equation describing the hyperbolic shape, we recommend reviewing the problem statement or any supporting materials for any missing details or measurements that could aid in determining the height of the tower.