An ellipsoid has radii with lengths of #15 #, #12 #, and #8 #. A portion the size of a hemisphere with a radius of #7 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-12-02T14:22:11

The remaining volume is #=5313.5u^3#

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

Here,

#a=15u#

#b=12u#

and #c=8u#

so,

#V_e=4/3pixx15xx12xx8=1920pi=6031.9u^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=2/3pixx7^3=718.4u^3#

The remaining volume is

#V_r=V_e-V_h=6031.9-718.4=5313.5u^3#