An ellipsoid has radii with lengths of #6 #, #9 #, and #4 #. 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 · 2016-10-10T20:10:39

The remaining volume is: #V =614/3pi#

I will give this reference for the Volume of an Ellipsoid

#V = 4/3piabc#

We are given #a = 6#, #b = 9#, and #c = 4#:

#V = 288pi#

I will give this reference for the Volume of a sphere

#V = 4/3pir^3#

For hemisphere, we must divide by 2:

#V = 4/6pir^3#

We are given #r = 5#:

#V = 250/3pi#

The remaining volume is the difference:

#V =614/3pi#