An ellipsoid has radii with lengths of #5 #, #4 #, and #8 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-08-14T18:22:18

#=613.65#

The Volume of an Ellipsoid with radii #=5,4 and 8#

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

#=pi/6(2times8)(2times4)(2times5)#

#=pi/6(16times8times10)#

#=(640pi)/3#

#=670.2#

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

#=2/3pitimes27#

#=18pi#

#=56.55#

So the remaining volume of the Ellipsoid

#=670.2-56.55#

#=613.65#