An ellipsoid has radii with lengths of 8, 4, and 7. A portion the size of a hemisphere with a radius of 3 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

1 Answer
Dec 3, 2017

The remaining volume is =881.8u3

Explanation:

The volume of an ellipsoid is Ve=43abc where a, b, and c are the lengths.

Here,

a=8u

b=4u

and c=7u

so,

Ve=43π×8×4×7=1920π=938.3u3

The volume of a hemisphere is Vh=23πr3 where r is rhe radius

Here,

r=7u

so,

Vh=23πr3=23π×33=56.5u3

The remaining volume is

Vr=VeVh=938.356.5=881.8u3