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

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Answer 1 · 2017-02-14T13:34:47

The remaining volume is $= 6.28 u^{3}$ $=6.28u^3$

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

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

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

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

$= \frac{2}{3} π \cdot 3$ $=2/3pi*3$

$= 6.28$ $=6.28$

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