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#