An ellipsoid has radii with lengths of $8$ $8$ , $4$ $4$ , and $7$ $7$ . 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 · 2017-12-03T12:55:45

The remaining volume is $= 881.8 u^{3}$ $=881.8u^3$

The volume of an ellipsoid is $V_{e} = \frac{4}{3} a b c$ $V_e=4/3abc$ where $a$ $a$ , $b$ $b$ , and $c$ $c$ are the lengths.

Here,

$a = 8 u$ $a=8u$

$b = 4 u$ $b=4u$

and $c = 7 u$ $c=7u$

so,

$V_{e} = \frac{4}{3} π \times 8 \times 4 \times 7 = 1920 π = 938.3 u^{3}$ $V_e=4/3pixx8xx4xx7=1920pi=938.3u^3$

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

Here,

$r = 7 u$ $r=7u$

so,

$V_{h} = \frac{2}{3} π r^{3} = \frac{2}{3} π \times 3^{3} = 56.5 u^{3}$ $V_h=2/3pir^3=2/3pixx3^3=56.5u^3$

The remaining volume is

$V_{r} = V_{e} - V_{h} = 938.3 - 56.5 = 881.8 u^{3}$ $V_r=V_e-V_h=938.3-56.5=881.8u^3$

An ellipsoid has radii with lengths of 88 , 44 , and 77 . 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?