Home > Geometry > Volume of Solids

An ellipsoid has radii with lengths of #3 #, #4 #, and #6 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Answer 1

Sadie Adams

The remaining volume is #=284.8u^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*3*4*6-2^3)#

#=2/3pi(144-8)#

#=2/3pi*136#

#=284.8#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Theodore Abad

The remaining volume of the ellipsoid after removing a hemisphere with a radius of 2 is approximately 219.8 cubic units.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.