An ellipsoid has radii with lengths of #6 #, #5 #, and #7 #. 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 8, 2016

#=427.25#

Explanation:

The Volume of an Ellipsoid
#=pi/6times#(major-axis)#times#(minor axis)#times#(vertcal-axis)
#=pi/6(2times6)(2times5)(2times7)#
#=pi/6(12times10times14)#
#=280pi#
#=879.65#
Volume of an Hemisphere#=2/3(pir^3)# where #r=6# is the radius
#=2/3pi(6)^3#
#=2/3pi(216)#
#=2pi(72)#
#=144pi#
#=452.4#
So the remaining volume of the Ellipsoid
#=879.65-452.4#
#=427.25#

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