An ellipsoid has radii with lengths of 6 6, 7 7, and 3 3. A portion the size of a hemisphere with a radius of 3 3 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

1 Answer
Aug 12, 2016

=471.3=471.3

Explanation:

The Volume of an Ellipsoid with radii =6,7 and 3=6,7and3

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

=pi/6(2times7)(2times3)(2times6)=π6(2×7)(2×3)(2×6)

=pi/6(14times6times12)=π6(14×6×12)

=168pi=168π

=527.8=527.8

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

=2/3pi(27)=23π(27)

=18pi=18π

=56.5=56.5

So the remaining volume of the Ellipsoid

=527.8-56.5=527.856.5

=471.3=471.3