# An ellipsoid has radii with lengths of #3 #, #4 #, and #7 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

THe answer is

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To find the volume of the remaining ellipsoid after removing a portion the size of a hemisphere with a radius of 3, we can use the formula for the volume of an ellipsoid:

[V = \frac{4}{3} \pi a b c]

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

Given that the ellipsoid originally has semi-axes lengths of 3, 4, and 7, and we remove a portion the size of a hemisphere with a radius of 3, the new semi-axes lengths will be 3, 4, and 4 (since the radius of the removed portion is the same as the semi-axis length of the ellipsoid).

Now we can calculate the volume of the remaining ellipsoid using the formula:

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

[V = \frac{4}{3} \pi \times 48]

[V ≈ 64 \pi]

So, the volume of the remaining ellipsoid is approximately (64 \pi).

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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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