An ellipsoid has radii with lengths of #9 #, #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 · 2017-12-05T10:41:29

The remaining volume is #=1149.9u^3#

The volume of an ellipsoid is #V_e=4/3abc# where #a#, #b#, and #c# are the lengths.

Here,

#a=9u#

#b=4u#

and #c=8u#

so,

#V_e=4/3pixx9xx4xx8=384pi=1206.4u^3#

The volume of a hemisphere is #V_h=2/3pir^3# where #r# is rhe radius

Here,

#r=7u#

so,

#V_h=2/3pir^3=2/3pixx3^3=56.5u^3#

The remaining volume is

#V_r=V_e-V_h=1206.4-56.5=1149.9u^3#