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

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Answer 1 · 2016-11-20T16:39:12

The remaining volume is $=1380.2$

The volume of an ellipsoid is $V_e=(4/3)piabc$

The volume of a hemisphere is $V_h=(2/3)pir^3$

The remaining volume $V_r=V_e-V_h$

$V_r=((2pi)/3)(2abc-r^3)$

$V_r=((2pi)/3)(2*8*7*7-5^3)$

$=(1318pi)/3=1380.2$

Answer 2 · 2016-11-20T16:42:31

$(1318 pi)/3$

Volume of an ellipsoid equals $4/3 pi abc$ . In this case it would be $4/3 pi *8*7*7= (1568 pi)/3$

Volume of an hemisphere is $2/3 pi r^3$ . In this case it would be $2/3 pi 5^3= (250 pi)/3$

The volume of the remaining solid would be $(1568pi)/3 - (250 pi)/3 =(1318 pi)/3$

An ellipsoid has radii with lengths of 8 8 , 7 7 , and 7 7 . 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?