An ellipsoid has radii with lengths of $6$ $6$ , $8$ $8$ , and $12$ $12$ . A portion the size of a hemisphere with a radius of $3$ $3$ is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

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Answer 1 · 2017-02-16T17:11:20

THe remaining volume is $= 2356.2 u^{3}$ $=2356.2u^3$

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

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

$= \frac{2}{3} π (2 \cdot 6 \cdot 8 \cdot 12 - 3^{3})$ $=2/3pi(2*6*8*12-3^3)$

$= \frac{2}{3} π (1152 - 27)$ $=2/3pi(1152-27)$

$= \frac{2}{3} π \cdot 1125$ $=2/3pi*1125$

$= 2356.2$ $=2356.2$

An ellipsoid has radii with lengths of 66 , 88 , and 1212 . A portion the size of a hemisphere with a radius of 33 is removed form the ellipsoid. What is the volume of the remaining ellipsoid?