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?

1 Answer
Apr 24, 2017

The remaining volume is 730/3pi7303π or 764.06764.06.

Explanation:

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=4/3piabcVE=43πabc, where V_E=VE=Volume of ellipsoid, pi=3.14π=3.14, and aa, bb, and cc are the radii.

The formula for volume of a hemisphere is:
V_H=2/3pir^3VH=23πr3, where V_H=VH=Volume of hemisphere, pi=3.14π=3.14, and r=r=radius.

Hence the remaining volume of the ellipsoid will be:

V_E-V_H=4/3piabc-2/3pir^3VEVH=43πabc23πr3

V_E-V_H=2/3pi(2abc-r^3)VEVH=23π(2abcr3)

V_E-V_H=2/3pi([2xx5xx7xx7]-[5^3])VEVH=23π([2×5×7×7][53])

V_E-V_H=2/3pi(490-125)VEVH=23π(490125)

V_E-V_H=2/3pixx365VEVH=23π×365

V_E-V_H=730/3piVEVH=7303π

V_E-V_H=730/3xx3.14VEVH=7303×3.14

V_E-V_H=764.06VEVH=764.06