A cooling tower for a nuclear reactor is to be constructed in the shape of a hyperboloid of one sheet. The diameter at the base is 260 m and the minimum diameter, 500 m above the base, is 180 m. Find an equation for the tower. (Assume the position of the hyperboloid is such that the center is at the origin with its axis along the z-axis, and the minimum diameter at the center.)

(x/90)² + (y/90)² - z²/343750

Step-by-step explanation:

we assume that the horizontal cross-sections are circles,

From our equation

a= b

Given the minimum diameter as 180

The trace= ,0

Minimum radius a= 180/2= 90

The base of the tower is the trace in Z = -500

using the equation of hyperbole of one sheet below

(x/a)² + (y/b)² - ( (z/c)²=1

a= 90

+((-500)²/c)²

x² +y²=90²+ 55000²/c²

diameter at base= 260/2=130m

130² + 55000²/c²= 130²

We can find c

c²=55000²/(130²/90²) = 1210000/8800

= 343750

hence, the equation is

(x/90)² + (y/90)² - z²/343750

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you