An ellipsoid has radii with lengths of #5 #, #5 #, 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?

Question

1747 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-20T10:04:07

The remaining volume is #=366.5u^3#

enter image source here

The volume of the ellipsoid is #V_e=4/3pi abc#

The volume of the hemisphere is #V_h=2/3pir^3#

The remaining volume is

#=V_e-V_h#

#=4/3piabc-2/3pir^3#

#=2/3pi(2abc-r^3)#

#=2/3pi(2*5*5*6-5^3)#

#=2/3pi*175#

#=366.5u^3#