# An ellipsoid has radii with lengths of #4 #, #9 #, and #5 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

So the remaining volume of the Ellipsoid

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The volume of the remaining ellipsoid after removing a hemisphere-sized portion can be calculated using the formula for the volume of an ellipsoid and then subtracting the volume of the hemisphere.

The formula for the volume of an ellipsoid is:

Volume = (4/3) * π * a * b * c

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

Given that the radii lengths are 4, 9, and 5, 'a', 'b', and 'c' are 4, 9, and 5 respectively.

The formula for the volume of a hemisphere is:

Volume = (2/3) * π * r^3

Where 'r' is the radius of the hemisphere.

Given that the radius of the hemisphere is 5, plug the values into the formulas to find the volumes:

Volume of ellipsoid = (4/3) * π * 4 * 9 * 5 Volume of hemisphere = (2/3) * π * 5^3

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

Volume of remaining ellipsoid = Volume of ellipsoid - Volume of hemisphere

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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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- Cups A and B are cone shaped and have heights of #25 cm# and #15 cm# and openings with radii of #7 cm# and #3 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?
- Two corners of an isosceles triangle are at #(9 ,4 )# and #(1 ,2 )#. If the triangle's area is #48 #, what are the lengths of the triangle's sides?
- The perimeter of the rectangular front lawn of the library is 192 feet. The ratio of the length to the width is 5:3. What is the area of the lawn?
- Three sides of a triangle are consecutive even integers and the perimeter of the triangle is 180 centimeters. What is the length of each of the three sides?

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