# An ellipsoid has radii with lengths of #8 #, #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?

The remaining volume is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the volume of the remaining ellipsoid after removing a portion the size of a hemisphere with a radius of 5, we first calculate the volume of the original ellipsoid using the formula:

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

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

Given that the lengths of the semi-axes of the original ellipsoid are 8, 9, and 5, respectively, we substitute these values into the formula:

[ V_{\text{original}} = \frac{4}{3} \pi \times 8 \times 9 \times 5 ]

Next, we calculate the volume of the hemisphere that was removed. The formula for the volume of a hemisphere is:

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

Given that the radius of the hemisphere is 5, we substitute this value into the formula:

[ V_{\text{hemisphere}} = \frac{2}{3} \pi \times 5^3 ]

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

[ V_{\text{remaining}} = V_{\text{original}} - V_{\text{hemisphere}} ]

Substitute the calculated values:

[ V_{\text{remaining}} = \left( \frac{4}{3} \pi \times 8 \times 9 \times 5 \right) - \left( \frac{2}{3} \pi \times 5^3 \right) ]

[ V_{\text{remaining}} = \left( \frac{4}{3} \pi \times 8 \times 9 \times 5 \right) - \left( \frac{2}{3} \pi \times 125 \right) ]

[ V_{\text{remaining}} = \left( \frac{4}{3} \pi \times 360 \right) - \left( \frac{250}{3} \pi \right) ]

[ V_{\text{remaining}} = \frac{1440}{3} \pi - \frac{250}{3} \pi ]

[ V_{\text{remaining}} = \frac{1190}{3} \pi ]

Therefore, the volume of the remaining ellipsoid is ( \frac{1190}{3} \pi ), or approximately 3962.2 cubic units.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- Archimedes found found an interesting property of arbelos, that is the area of the circle whose diameter is AH and has common tangent line to the two smaller semicircles at point A is equal to the shaded area. Prove it?
- Two corners of an isosceles triangle are at #(4 ,2 )# and #(5 ,7 )#. If the triangle's area is #3 #, what are the lengths of the triangle's sides?
- How do you find diameter from the circumference of a circle?
- A triangle has two corners with angles of # ( pi ) / 4 # and # ( 7 pi )/ 12 #. If one side of the triangle has a length of #6 #, what is the largest possible area of the triangle?
- The diameter of a circle is 4 miles. What is the circle's radius?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7