An ellipsoid has radii with lengths of #8 #, #6 #, and #5 #. A portion the size of a hemisphere with a radius of #6 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Question

An ellipsoid has radii with lengths of #8   #, #6  #, and #5  #. A portion the size of a hemisphere with a radius of #6  # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Avery Allen · Accepted Answer

The answer is #=552.9 u^3# Volume of ellipsoid is #=4/3piabc# Volume of henisphere is #=2/3pir^3# Remaining volume #=4/3piabc-2/3pir^3# #=2/3pi(2abc-r^3)# #=2/3pi(2*8*6*5-6^3)# #=2/3pi(480-216)# #=2/3pi*264# #=552.9#

Evelyn Arboleda · Answer

undefined To find the volume of the remaining ellipsoid after removing a portion the size of a hemisphere with a radius of 6, we can use the formula for the volume of an ellipsoid:

Volume = (4/3)πabc

Where a, b, and c are the radii of the ellipsoid.

Given:
a = 8
b = 6
c = 5

The volume of the original ellipsoid is:
V_original = (4/3)π(8)(6)(5)

To find the volume of the removed hemisphere, we use the formula for the volume of a hemisphere:

V_hemisphere = (2/3)πr³

Where r is the radius of the hemisphere.

Given:
r = 6

V_hemisphere = (2/3)π(6)³

The volume of the remaining ellipsoid is the volume of the original ellipsoid minus the volume of the removed hemisphere:

V_remaining = V_original - V_hemisphere