An ellipsoid has radii with lengths of #6 #, #5 #, and #3 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

1 Answer
Deepak G.
Aug 16, 2016

Since the volume of the Volume of the Hemisphere is larger than the volume of the Ellipsoid.
Therefore it is not possible to remove the Hemisphere of the size given#(r=6)#

Explanation:

The Volume of an Ellipsoid with radii #=6,5 and 3#

#=pi/6times#(major-axis)#times#(minor axis)#times#(vertcal-axis)

#=pi/6(2times6)(2times3)(2times5)#

#=pi/6(12times6times10)#

#=120pi#

#=377#

Volume of an Hemisphere#=2/3(pir^3)# where #r=6# is the radius
#=2/3pi(6)^3#

#=2/3pitimes216#

#=144pi#

#=452.4#

Since the volume of the Volume of the Hemisphere is larger than the volume of the Ellipsoid.
Therefore it is not possible to remove the Hemisphere of the size given#(r=6)#

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