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

Volume=56π3

Explanation:

The volume of an ellipsoid is given by:

V=43πabc

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=43πr3

So volume of hemisphere is:

V=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=43πabc23πr3

V=23π(2abcr3)

Substituting values:

V=23π(233223)

V=23π(28)

V=56π3