A hyperboloid cooling tower is 400 feet wide at its base and is 350 feet wide at its narrowest point and 400 feet above the ground. What is the equation of the hyperboloid that models the shape of the tower?

Answer 1

The figure's base is the circle x^2+y^2 = 200^2 at z = -400
The equation of the hyperboloid is
x^2/175^2 + y^2/175^2 - z^2/c^2 = 1
and contains the point (200,0,-400)
so that makes it
x^2/175^2 + y^2/175^2 - z^2/(560 √(5/3))^2 = 1