Spherical tank

The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?

Correct result:

h =  22.8446 ft

Solution:

r=35 ft  V=43⋅ π⋅ r3=43⋅ 3.1416⋅ 353≐179594.38 ft3  V1=14⋅ V=14⋅ 179594.38≐44898.595 ft3  V2=π⋅ h23(3r−h)  V1=V2 π⋅ r33=π⋅ h23(3r−h) r3=h2(3r−h)  h1=−18.6231 h2=22.8446 h3=100.778  0<h<2r  h=h2=22.8446=22.8446 ft  V2=π⋅ h23⋅ (3⋅ r−h)=3.1416⋅ 22.844623⋅ (3⋅ 35−22.8446)≐44898.5017 ft3

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