Volume of a ring

Calculus Level 5

The figure above is a ring generated by rotating an ellipse around an axis. The ellipse has major axis \(3.5\text{ mm}\) and minor axis \(1.5 \text{ mm}\). The axis of rotation is parallel to the major axis of the ellipse, and is \(10\text{ mm}\) away from the center of the ellipse.

What is the volume of the ring (in \(\text{mm}^3\)) rounded to three decimal places?

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