Question

The vertical cross-section of a nuclear power plant's cooling tower is in the shape of a hyperbola. Suppose the tower has a base diameter of 204 meters and the diameter at its narrowest point, 72 meters above the ground, is 68 meters. The top of the tower has a diameter of 102 meters, and the height of the tower is 108 meters.

Use the key points that you found in the previous part of this lab and the Quadratic Regression feature in your graphing calculator to find the equation of the function that you will be revolving about the x-axis, to form the solid of revolution. The equation found is y =x2 + _x + _. (Round your values to five decimals, if needed.)

Answer 1

the tower has a base diameter of 204 meters

and the diameter at its narrowest point, 72 meters above the ground,

is 68 meters.

The top of the tower has a diameter of 102 meters,

and the height of the tower is 108 meters.

center at origin ( 0,0 )

right endpoint of base ( 102 , - 72 )

using hyperbola equation ( x²/a² ) - ( y²/b² ) = 1

2 a = 68

a = 34

a² = 1156

102² / 1156 - 72² / b² = 1

72² / b² = 102² / 1156 - 1

72² / b² = 8

b² = 648

so hyperbola equation ( x²/a² ) - ( y²/b² ) = 1

then ( x²/1156 ) - ( y²/648 ) = 1

x = 68

then

( 68²/1156 ) - ( y²/648 ) = 1

y²/648 = ( 68²/1156 ) - 1

y²/648 = 3

y = 44.09

so the height of the tower is = y + 72

= 44.09 + 72

the height of the tower is = 116.0908154 m