An ellipsoid has radii with lengths of 3 3, 8 8, and 8 8. A portion the size of a hemisphere with a radius of 3 3 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

1 Answer
Jun 13, 2018

color(blue)("Volume"=238pi " units"^3)Volume=238π units3

Explanation:

The volume of an ellipsoid is given by:

V=4/3pi*a*b*cV=43πabc

Where a, b, ca,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^3V=43πr3

So volume of hemisphere is:

V=2/3pir^3V=23πr3

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^3V=43πabc23πr3

V=2/3pi(2abc-r^3)V=23π(2abcr3)

Substituting values:

V=2/3pi(2*3*8*8-3^3)V=23π(238833)

V=2/3pi(357)V=23π(357)

V=238piV=238π