An ellipsoid has radii with lengths of #4 #, #9 #, and #5 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Question

An ellipsoid has radii with lengths of #4   #, #9  #, and #5  #. A portion the size of a hemisphere with a radius of #5  # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

Sophia Alfred · Accepted Answer

#=492.2#

The Volume of an Ellipsoid with radii #=4,9 and 5#

#=pi/6times#(major-axis)#times#(minor axis)#times#(vertcal-axis)

#=pi/6(2times9)(2times4)(2times5)#

#=pi/6(18times8times10)#

#=240pi#

#=754#

Volume of an Hemisphere#=2/3(pir^3)# where #r=5# is the radius #=2/3pi(5)^3#

#=2/3pitimes125#

#=(250pi)/3#

#=261.8#

So the remaining volume of the Ellipsoid

#=754-261.8#

#=492.2#

Savannah Aguilar · Answer

undefined The volume of the remaining ellipsoid after removing a hemisphere-sized portion can be calculated using the formula for the volume of an ellipsoid and then subtracting the volume of the hemisphere.

The formula for the volume of an ellipsoid is:

Volume = (4/3) * π * a * b * c

Where 'a', 'b', and 'c' are the semi-axes lengths of the ellipsoid.

Given that the radii lengths are 4, 9, and 5, 'a', 'b', and 'c' are 4, 9, and 5 respectively.

The formula for the volume of a hemisphere is:

Volume = (2/3) * π * r^3

Where 'r' is the radius of the hemisphere.

Given that the radius of the hemisphere is 5, plug the values into the formulas to find the volumes:

Volume of ellipsoid = (4/3) * π * 4 * 9 * 5
Volume of hemisphere = (2/3) * π * 5^3

Now, subtract the volume of the hemisphere from the volume of the ellipsoid to find the volume of the remaining ellipsoid:

Volume of remaining ellipsoid = Volume of ellipsoid - Volume of hemisphere