An ellipsoid has radii with lengths of 12 12, 16 16, and 8 8. A portion the size of a hemisphere with a radius of 8 8 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

1 Answer
Aug 13, 2016

=5361.67=5361.67

Explanation:

The Volume of an Ellipsoid with radii =12,16 and 8=12,16and8

=pi/6times=π6×(major-axis)times×(minor axis)times×(vertcal-axis)

=pi/6(2times16)(2times8)(2times12)=π6(2×16)(2×8)(2×12)

=pi/6(32times16times24)=π6(32×16×24)

=2048pi=2048π

=6434=6434

Volume of an Hemisphere=2/3(pir^3)=23(πr3) where r=8r=8 is the radius
=2/3pi(8)^3=23π(8)3

=2/3pitimes512=23π×512

=341.34pi=341.34π

=1072.34=1072.34

So the remaining volume of the Ellipsoid

=6434-1072.34=64341072.34

=5361.67=5361.67