An ellipsoid has radii with lengths of $9$ $9$ , $16$ $16$ , and $4$ $4$ . A portion the size of a hemisphere with a radius of $8$ $8$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-03-02T07:35:44

The remaining volume is $= 1340.4 u^{3}$ $=1340.4u^3$

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

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

$= \frac{2}{3} π (2 \cdot 9 \cdot 16 \cdot 4 - 8^{3})$ $=2/3pi(2*9*16*4-8^3)$

$= \frac{2}{3} π (1152 - 512)$ $=2/3pi(1152-512)$

$= \frac{2}{3} π \cdot 640$ $=2/3pi*640$

$= 1340.4$ $=1340.4$

An ellipsoid has radii with lengths of 99 , 1616 , and 44 . A portion the size of a hemisphere with a radius of 88 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?