An ellipsoid has radii with lengths of #14 #, #11 #, and #7 #. A portion the size of a hemisphere with a radius of #9 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Question

An ellipsoid has radii with lengths of #14   #, #11  #, and #7  #. A portion the size of a hemisphere with a radius of #9  # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Theodore Abad · Accepted Answer

#2988.702\ ext{unit}^3# The volume #V# of ellipsoid of radii #a=14, b=11# & #c=7# is given as #V={4\pi}/3abc# #={4\pi}/3(14)(11)(7)# #={4312\pi}/3# The volume #V_1# of hemisphere of radius #r=9# is given as #V_1=1/2({4\pi}/3r^3)# #={2\pi}/3r^3# #={2\pi}/3(9)^3# #=486\pi# thus the ellipsoid volume after the hemisphere's volume is subtracted. #=V-V_1# #={4312\pi}/3-486\pi# #={2854\pi}/3# #=2988.702\ ext{unit}^3#

Theodore Abad · Answer

undefined To find the remaining volume of the ellipsoid after removing a hemisphere with a radius of 9, we first calculate the volume of the ellipsoid using the formula $V = \frac{4}{3} \pi abc$, where $a$, $b$, and $c$ are the semi-axes lengths.

Then, we calculate the volume of the removed hemisphere using the formula $V_{\text{hemisphere}} = \frac{2}{3} \pi r^3$, where $r$ is the radius of the hemisphere.

Finally, we subtract the volume of the hemisphere from the volume of the ellipsoid to find the remaining volume.