Spherical tank

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

Correct answer:

h =  22.8446 ft

Step-by-step explanation:

r=35 ft  V=34​⋅ π⋅ r3=34​⋅ 3.1416⋅ 353≐179594.38 ft3  V1​=41​⋅ V=41​⋅ 179594.38≐44898.595 ft3  V2​ = 3π⋅ h2​(3r−h)  V1​ = V2​ 3π⋅ r3​ = 3π⋅ h2​(3r−h) r3 = h2(3r−h) 42875 = (105 − h) h2 h3 − 105 h2 + 42875 = 0  h1​=−18.6231 h2​=22.8446 h3​=100.778  0 < h < 2r  h=h2​=22.8446=22.8446 ft   Verifying Solution:   V2​=3π⋅ h2​⋅ (3⋅ r−h)=33.1416⋅ 22.84462​⋅ (3⋅ 35−22.8446)≐44898.5017 ft3

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Showing 1 comment:
Math student
ca you show me the step by step of the height

4 years ago  3 Likes




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