Problem #35

A Reuleaux triangle is constructed by taking an equilateral triangle ABC and drawing the three circular arcs: BC with center A, AC with center B, and AB with center C, as shown below. The Reuleaux triangle is an example of a "curve of constant width".
This month's problem is to find the volume and the surface area of the solid obtained by rotating the Reuleaux triangle shown above around a vertical axis passing through vertex A. Express your answer in terms of r, the length of a side of the original equilateral triangle.

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