An ellipsoid has radii with lengths of $8$ $8$ , $7$ $7$ , and $6$ $6$ . A portion the size of a hemisphere with a radius of $5$ $5$ is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

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Answer 1 · 2017-02-05T07:51:03

The volume is $= 1145.6 u^{3}$ $=1145.6 u^3$

Volume of ellipsoid is $= \frac{4}{3} π a b c$ $=4/3piabc$

Volume of henisphere is $= \frac{2}{3} π r^{3}$ $=2/3pir^3$

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

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

$= \frac{2}{3} π (2 \cdot 8 \cdot 7 \cdot 6 - 5^{3})$ $=2/3pi(2*8*7*6-5^3)$

$= \frac{2}{3} π (672 - 125)$ $=2/3pi(672-125)$

$= \frac{2}{3} π \cdot 547$ $=2/3pi*547$

$= 1145.6$ $=1145.6$

An ellipsoid has radii with lengths of 8 88 , 7 77 , and 6 66 . A portion the size of a hemisphere with a radius of 5 55 is removed form the ellipsoid. What is the remaining volume of the ellipsoid?