An ellipsoid has radii with lengths of 12 12, 11 11, and 8 8. A portion the size of a hemisphere with a radius of 9 9 is removed from the ellipsoid. What is the remaining volume of the ellipsoid?

1 Answer
Apr 12, 2017

The remaining volume is 922pi922π or 2897.712897.71.

Explanation:

The formula for the volume of an ellipsoid where the three radii are represented by aa, bb, and cc, is:

V_E=4/3piabcVE=43πabc

In the given case:

V_E=4/3pixx12xx11xx8VE=43π×12×11×8

The formula for volume of a hemisphere is:

V_H=2/3pir^3VH=23πr3

In the given case:

V_H=2/3pixx9^3VH=23π×93

V_H=2/3pixx729VH=23π×729

We need to determine the volume of the ellipsoid when the hemisphere is removed from it, which is;

V_E-V_H=(4/3pixx12xx11xx8)-(2/3pixx729)VEVH=(43π×12×11×8)(23π×729)

Simplify the brackets.

V_E-V_H=(4/cancel3pixx4cancel12xx11xx8)-(2/cancel3pixx243cancel729)

V_E-V_H=(4pixx4xx11xx8)-(2pixx243)

V_E-V_H=1408pi-486pi

V_E-V_H=(1408-486)pi

V_E-V_H=922pi

Considering pi as 22/7, we get:

V_E-V_H=922xx22/7

V_E-V_H=2897.71