An ellipsoid has radii with lengths of #15 #, #12 #, and #9 #. A portion the size of a hemisphere with a radius of #7 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

Answer 1

#6067.4626\ \text{unit}^3#

The remaining volume of the ellipsoid will be equal to the difference of volume of original ellipsoid with radii #a=15#, #b=12# & #c=9# & the volume of hemi-sphere of radius #r=7# hence the remaining volume of ellipsoid
#\frac{4\pi}{3}abc-2/3\pir^3#
#=\frac{4\pi}{3}(15)(12)(9)-2/3\pi(7)^3#
#=\frac{5794\pi}{3}#
#=6067.4626\ \text{unit}^3#
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Answer 2

The remaining volume of the ellipsoid after removing a hemisphere with a radius of 7 units is approximately 3754.9 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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