An ellipsoid has radii with lengths of 2 2, 7 7, and 4 4. 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 11, 2016

~=178178

Explanation:

The Volume of an Ellipsoid with radii =2,7 and 4=2,7and4

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

=pi/6(2times7)(2times2)(2times4)=π6(2×7)(2×2)(2×4)

=pi/6(14times4times8)=π6(14×4×8)

=74.67pi=74.67π

=234.57=234.57

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

=234.57-56.5=234.5756.5

~=178178