Volume of Ellipse No idea how to do this

In summary, the volume of an ellipse can be found using the formula V = (4/3) * π * a * b * c, and it cannot be negative. The lengths of the axes can be determined using the formula a^2 = b^2 + c^2. The volume is not affected by the orientation of the ellipse and can be greater than the volume of a sphere due to its dependence on three axes.
  • #1
ruri
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Homework Statement



Rotating the ellipse x^2/a^2 + y^2/b^2 = 1 about the x-axis generates and ellipsoid. Compute its volume.

Homework Equations





The Attempt at a Solution

 
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  • #2
You can do it several ways. One way to do it is to observe that if you rotate only the upper half of the ellipse you still get the same ellipsoid. Then slice it vertically. What is the positive value of y for each x? The rotation of each slice will be a disc. Integrate the volume of the discs to get the entire volume of the ellipsoid.
 

Related to Volume of Ellipse No idea how to do this

1. What is the formula for finding the volume of an ellipse?

The formula for finding the volume of an ellipse is V = (4/3) * π * a * b * c, where a, b, and c are the lengths of the three axes of the ellipse.

2. Can the volume of an ellipse be negative?

No, the volume of an ellipse cannot be negative. It is a measurement of three-dimensional space, which can only have positive values.

3. How do I find the lengths of the axes for an ellipse?

The lengths of the axes for an ellipse can be found by using the formula a^2 = b^2 + c^2, where a is the length of the semi-major axis, and b and c are the lengths of the semi-minor axes.

4. Is the volume of an ellipse affected by its orientation?

No, the volume of an ellipse is not affected by its orientation. As long as the lengths of the axes remain the same, the volume will remain constant.

5. Can the volume of an ellipse be greater than the volume of a sphere?

Yes, the volume of an ellipse can be greater than the volume of a sphere. This is because the volume of an ellipse is dependent on the lengths of its three axes, while the volume of a sphere is only dependent on its radius.

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