Question

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?

Answer 1

`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!