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