An ellipsoid has radii with lengths of $2$ $2$ , $5$ $5$ , 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?

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Answer 1 · 2017-03-01T06:54:16

The remaining volume is $= 111 u^{3}$ $=111 u^3$

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

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

$= \frac{2}{3} π (2 \cdot 2 \cdot 5 \cdot 4 - 3^{3})$ $=2/3pi(2*2*5*4-3^3)$

$= \frac{2}{3} π (80 - 27)$ $=2/3pi(80-27)$

$= \frac{2}{3} π \cdot 53$ $=2/3pi*53$

$= 111$ $=111$

An ellipsoid has radii with lengths of 22 , 55 , and 44 . A portion the size of a hemisphere with a radius of 33 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?