An ellipsoid has radii with lengths of $5$ $5$ , $5$ $5$ , 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 · 2017-07-20T10:04:07

The remaining volume is $= 366.5 u^{3}$ $=366.5u^3$

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The volume of the ellipsoid is $V_{e} = \frac{4}{3} π a b c$ $V_e=4/3pi abc$

The volume of the hemisphere is $V_{h} = \frac{2}{3} π r^{3}$ $V_h=2/3pir^3$

The remaining volume is

$= V_{e} - V_{h}$ $=V_e-V_h$

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

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

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

$= \frac{2}{3} π \cdot 175$ $=2/3pi*175$

$= 366.5 u^{3}$ $=366.5u^3$

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