An ellipsoid has radii with lengths of #3 #, #3 #, and #2 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

1 Answer
Jun 6, 2018

#color(blue)("Volume"=(56pi)/3)#

Explanation:

The volume of an ellipsoid is given by:

#V=4/3pi*a*b*c#

Where #a, b, c are the radii of the ellipsoid.

The volume of a hemisphere is half the volume of a sphere:

Volume of a sphere is:

#V=4/3pir^3#

So volume of hemisphere is:

#V=2/3pir^3#

To find the volume of the ellipsoid when the hemisphere is removed, we just find the volume of the ellipsoid and subtract the volume of the hemisphere:

#V=4/3pi*a*b*c-2/3pir^3#

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

Substituting values:

#V=2/3pi(2*3*3*2-2^3)#

#V=2/3pi(28)#

#V=(56pi)/3#