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

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Answer 1 · 2017-04-24T13:52:36

The remaining volume is $730/3pi$ or $764.06$ .

To determine the remaining volume of the ellipsoid, we need to subtract the volume of the hemisphere from the volume of the ellipsoid.

The formula for volume of an ellipsoid is:
$V_E=4/3piabc$ , where $V_E=$ Volume of ellipsoid, $pi=3.14$ , and $a$ , $b$ , and $c$ are the radii.

The formula for volume of a hemisphere is:
$V_H=2/3pir^3$ , where $V_H=$ Volume of hemisphere, $pi=3.14$ , and $r=$ radius.

Hence the remaining volume of the ellipsoid will be:

$V_E-V_H=4/3piabc-2/3pir^3$

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

$V_E-V_H=2/3pi([2xx5xx7xx7]-[5^3])$

$V_E-V_H=2/3pi(490-125)$

$V_E-V_H=2/3pixx365$

$V_E-V_H=730/3pi$

$V_E-V_H=730/3xx3.14$

$V_E-V_H=764.06$

An ellipsoid has radii with lengths of 55, 77, and 77. A portion the size of a hemisphere with a radius of 55 is removed from the ellipsoid. What is the remaining volume of the ellipsoid?