An ellipsoid has radii with lengths of $3$ $3$ , $4$ $4$ , and $1$ $1$ . A portion the size of a hemisphere with a radius of $2$ $2$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Question

1218 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-10T09:26:58

The remaining volume is $= 33.5 u^{3}$ $=33.5 u^3$

Volume of ellipsoid is $= \frac{4}{3} π a b c$ $=4/3piabc$

Volume of hemisphere is $= \frac{2}{3} π r^{3}$ $=2/3pir^3$

Remaining volume $= \frac{4}{3} π a b c - \frac{2}{3} π r^{3}$ $=4/3piabc-2/3pir^3$

$= \frac{2}{3} π (2 a b c - r^{3})$ $=2/3pi(2abc-r^3)$

$= \frac{2}{3} π (2 \cdot 3 \cdot 4 \cdot 1 - 2^{3})$ $=2/3pi(2*3*4*1-2^3)$

$= \frac{2}{3} π (24 - 28)$ $=2/3pi(24-28)$

$= \frac{2}{3} π \cdot 16$ $=2/3pi*16$

$= 33.5$ $=33.5$

An ellipsoid has radii with lengths of 3 33 , 4 44 , and 1 11 . A portion the size of a hemisphere with a radius of 2 22 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?