# An ellipsoid has radii with lengths of #9 #, #11 #, and #4 #. A portion the size of a hemisphere with a radius of #8 # is removed form the ellipsoid. What is the remaining volume of the ellipsoid?

#560/3 pi~~586.43#

since it is essentially a sphere's volume that has been stretched or compressed in a few dimensions.

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To find the remaining volume of the ellipsoid after removing a portion the size of a hemisphere with a radius of 8, you can calculate the volume of the ellipsoid and subtract the volume of the removed portion.

The formula for the volume of an ellipsoid is given by:

[ V = \frac{4}{3} \pi abc ]

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

Given that the radii lengths of the ellipsoid are 9, 11, and 4, respectively, we have (a = 9), (b = 11), and (c = 4).

Now, we calculate the volume of the ellipsoid:

[ V_{\text{ellipsoid}} = \frac{4}{3} \pi \times 9 \times 11 \times 4 ]

Next, we need to calculate the volume of the removed portion, which is a hemisphere with a radius of 8. The formula for the volume of a hemisphere is:

[ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 ]

Where ( r = 8 ).

[ V_{\text{hemisphere}} = \frac{2}{3} \pi \times 8^3 ]

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

[ \text{Remaining volume} = V_{\text{ellipsoid}} - V_{\text{hemisphere}} ]

You can perform the calculations to find the numerical value of the remaining volume.

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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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