the volume of a spherical segment with base radius, r and height, h, is given by the formula v= 1/6 pie*h (3r^2+h^2)a domed stadium is in the shape...

V = (1/6)pi * h(3r^2 + h^2)

r
= 150 m

v= 3,500,000 m^3

To
find the height we will substitue in v"

V = (1/6) pi *h
(3r^2 + h^2)

3,500,000 = (1/6)*pi *h (3(150^2) +
h^2)

Multiply by
6/pi

==> 3,500,000*6/ (22/7) = h(3*(150^2) +
h^2)

==> h(67,500 + h^2) = 21,000,000/
(22/7)

==:> h^2 + 67,500 h - 21,000,000*7/22 =
0

Multiply by 22:

==>
22h^2 + 1485,000h  -  147,000,000 = 0

Divide by
2:

==> 11h^2 + 742,500 h - 73,500,000 =
0

==> h= [-742,500 + sqrt(742,500^2 +
4*11*73,500,00]/22

          = 98.8
m

Then the height h = 98.8 m