An ellipsoid has radii with lengths of $6$ $6$ , $8$ $8$ , and $5$ $5$ . A portion the size of a hemisphere with a radius of $6$ $6$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-02-13T14:04:00

The remaining volume is $= 552.9 u^{3}$ $=552.9 u^3$

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

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

$= \frac{2}{3} π (2 \cdot 6 \cdot 8 \cdot 5 - 6^{3})$ $=2/3pi(2*6*8*5-6^3)$

$= \frac{2}{3} π (480 - 216)$ $=2/3pi(480-216)$

$= \frac{2}{3} π \cdot 264$ $=2/3pi*264$

$= 552.9$ $=552.9$

An ellipsoid has radii with lengths of 66 , 88 , and 55 . A portion the size of a hemisphere with a radius of 66 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?