An ellipsoid has radii with lengths of $12$ , $16$ , and $7$ . A portion the size of a hemisphere with a radius of $8$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Question

1153 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-29T11:02:56

The volume is $=4557.4 u^3$

Volume of ellipsoid is $=4/3piabc$

Volume of henisphere is $=2/3pir^3$

Remaining volume $=4/3piabc-2/3pir^3$

$=2/3pi(2abc-r^3)$

$=2/3pi(2*12*16*7-8^3)$

$=2/3pi(2688-512)$

$=2/3pi*2176$

$=4557.4$

An ellipsoid has radii with lengths of 12 12 , 16 16 , and 7 7 . 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?