Stadium

A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.

Correct result:

x =  88.7 m

Solution:

V=3500000 V=πh/6 (3r2+h2) 6V/π=h(3r2+h2) h3+67500 h(6V/π)=0 h3+67500h6684507.60899=0  h1=88.693342641488.6933 h2=44.3466713+270.9241255i h3=44.3466713270.9241255i  h>0  x=h1=88.6933=88.7 m

Equation is non-linear.
Equation is not quadratic.
h3+67500h6684507.60899=0h^3+67500h-6684507.60899=0
h1 = 88.693342641435
h2 = -44.3466713+270.9241255i
h3 = -44.3466713-270.9241255i

Our simple equation calculator calculates it.



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