a) What are the area and circumference of the circular base of the tower? b) What is the width of the tower at its narrowest point?

Question

The cross-section of a nuclear reactor cooling tower is in the shape of a hyperbola

described by the equation

x²/5625 - y²/30625 = 1

The height of the tower is 250 feet from the ground to the transverse axis of the

hyperbola.

Answer 1

To find radius at base let y = 0. Then x^2/5625 = 1. Solve for x to get x = 75.

The area of base is Pi (75)^2 = 1761

The circumference is 2Pi (75) = 471

The width at narrowest point is twice the base radius = 150