An ellipsoid has radii with lengths of #8 #, #6 #, and #4 #. A portion the size of a hemisphere with a radius of #2 # is removed from the ellipsoid. What is the volume of the remaining ellipsoid?

1 Answer
Parabola
Jan 28, 2018

#250 2/3pi=V#

Explanation:

Remember that the formula for the volume of an ellipsoid is:
#V=4/3pi(r_1*r_2*r_3)#

We plug the given radii lengths to find the volume.

=>#V=4/3pi(8*6*4)#
=>#V=4/3pi192#
=>#V=256pi#

Now, a hemisphere with a radius of 2 is removed from the ellipsoid.
We have to subtract the volume of the hemisphere from the volume of the ellipsoid.

A volume of a hemisphere is: #1/2*4/3*pir^3# We now solve for the volume.
=>#V=1/2*4/3*pir^3#
=>#V=4/6*pi(2)^3#
=>#V=4/6*pi8#
=>#V=16/3*pi# We now subtract.

=>#256pi-16/3pi=V#

=>#pi(256-16/3)=V#
=>#pi(752/3)=V#
=>#250 2/3pi=V#
That is our answer!

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