An ellipsoid has radii with lengths of #8 #, #7 #, and #7 #. 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 · 2016-11-20T16:39:12

The remaining volume is #=1380.2#

The volume of an ellipsoid is #V_e=(4/3)piabc#

The volume of a hemisphere is #V_h=(2/3)pir^3#

The remaining volume #V_r=V_e-V_h#

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

#V_r=((2pi)/3)(2*8*7*7-5^3)#

#=(1318pi)/3=1380.2#

Answer 2 · 2016-11-20T16:42:31

#(1318 pi)/3#

Volume of an ellipsoid equals #4/3 pi abc#. In this case it would be #4/3 pi *8*7*7= (1568 pi)/3 #

Volume of an hemisphere is #2/3 pi r^3 #. In this case it would be #2/3 pi 5^3= (250 pi)/3#

The volume of the remaining solid would be #(1568pi)/3 - (250 pi)/3 =(1318 pi)/3#