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Question 33720: A storage bulding for rock salt has the shape of a paraboloid which has vertical cross sections that are parabolas. The equation of a vertical cross section is y=(-1/2)x^2. If the building is 27 feet high, how much rock salt will it hold? (Hint: The volume of a paraboloid is v=(1/2)[pi]r^2h where r=radius of base and h=height.)
Hope that makes sense! Thanks! :)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Consider the shape of y=(-1/2)x^2+27, which has the same shape
as yours. Find the x-intercepts to determine the radius of
the building, as follows:
(1/2)x^2=27
x^2=54
x=radius=sqrt27
Then Volume = (1/2)(pi)(radius)^2(height)
V= (1/2)(pi)54(27)
V=27^2(pi)
Volume=729pi cu.ft.
Cheers,
Stan H.
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