An ellipsoid has radii with lengths of #6 #, #7 #, and #6 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2016-11-09T23:09:48

The remaining volume is:
#V_r ~~ 794" units"^3 #

#V = 4/3piabc# where a, b, and c are the radii.

#V = 4/3pi(6)(7)(6)#

#V = 4/3pir^3#

The volume of the hemisphere is half of that:

#V = 4/6pi5^3#

The remaining volume is the difference:

#V_r = 4/3pi(6(7)(6) - 5^3/2)#

#V_r ~~ 794" units"^3 #