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A uniform solid spinning top has the shape of an inverted right circular cone of radius 3r and height 4r surmounted by a right circular of base radius 3r and height 6r. Find the position of the centre of mass of the spinning top and hence show that if it is placed with the curved surface of the cone on a horizontal plane the top will topple.

This is my answer

y = 0 by symmetry

54[Pi]r^3 (3r) + 3[Pi]r^2 (7r) = [54 [Pi] r^3 + 3[Pi] r^2] x

54r^2 + 7r = (18r + 1) x

x = (54 r^2 + 7r) /(18r +1)

But the text book says the answer is (75/33)r from joint face

Please Help me.

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# This is driving me nuts

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