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There's a solid which is a result of revolution of a rhombus by the axis which is paralell to the shorter diagonal and goes through the end-point of a longer diagonal. Longer diagonal is $\frac2{\sqrt{3}}$, sides are 2 and the angle between diagonals and sides is $60^{\circ}$. Calculate its volume.

I thought of using Pappus-Guldin theorem - area of rhombus multiplied by the perimeter of circle with radius made of longer diagonal. Is this a proper or I should divide it to cones?

P.S: Sorry for my english, I've never written anything related to math in this language until now.

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According to the Pappus-Guldin (second) theorem the volume would be equal to the area of the rhombus times the distance travelled by its centroid which is obviously located at the intersection of the diagonals. Thus half of the larger diagonal must be taken as the radius.

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I was wondering if I should use half of the larger diagonal or it whole. Thanks for clarification on this theorem! – metrampaz Dec 17 '12 at 16:08

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