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

Answer 1

The remaining volume is #=552.9 u^3#

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

The remaining volume of the ellipsoid after removing a portion the size of a hemisphere with a radius of 6 is approximately 536.94 cubic units.

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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.

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.

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.

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.

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