An ellipsoid has radii with lengths of 15 , 12 , and 9 . A portion the size of a hemisphere with a radius of 7 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

1 Answer

6067.4626\ \text{unit}^3

Explanation:

The remaining volume of the ellipsoid will be equal to the difference of volume of original ellipsoid with radii a=15, b=12 & c=9 & the volume of hemi-sphere of radius r=7 hence the remaining volume of ellipsoid

\frac{4\pi}{3}abc-2/3\pir^3

=\frac{4\pi}{3}(15)(12)(9)-2/3\pi(7)^3

=\frac{5794\pi}{3}

=6067.4626\ \text{unit}^3