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A hydrometer is a device that measures the density of a liquid. The one shown in the figure has a cylindrical bulb of radius R attached to a cylindrical stem of radius r and length l. When placed in a liquid, the device floats as shown in the figure with a length h of stem protruding. Given that the mass of the hydrometer is M, find the density ρ of the liquid. Express your answer in terms of M ,R, r ,l and h (enter M for M, R for R, r for r, l for l, h for h and pi for π).

ρ=

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M/(pi*r^2*(l-h) + 4*pi*R^3/3)

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