As shown in the figure, the rectangular coordinate system is established with the highest point of the dome as the origin, and the parabolic equation is set to y = kx 2, and k < 0.

Points a and b are the outermost parts of the parabolic dome.

Obviously AB = 150m, and the abscissas of A and B are -75 and 75 respectively.

CD is the skylight. Obviously, the abscissas of c and d are -28 and 28 respectively.

Since the origin is the highest point of the building, point C is 33.8-33 = 0.8 lower than the highest point.

Then the ordinate of C and D is -0.8, and the coordinate of point C is (-28, -0.8).

Substitute into parabolic equation

-0.8=k*28*28

solve

K =-0.00 102, so the analytical formula of parabola is

y=-0.00 102x^2

(2)

Then find the ordinate ye=30-33.8=-3.8 (assuming that the point is E) of the point 30m above the ground and substitute it into the parabolic equation.

Xe xe= 6 1.0368。

So the diameter is 2 | xe | = 122.0735.

(3)

The entire dome is of the same height. Find the ordinate of a and b and substitute it into the abscissa of a.

ya=-5.7375

So the height of the whole dome is 0-(-5.7375) = 5.7375 m.