A hollow sphere of inner radius 8.0 cm and outer radius 9.0 cm floats half submerged in a liquid of specific gravity 0.80. Calculate the density of the material of which the sphere is made.(adsbygoogle = window.adsbygoogle || []).push({});

Density of water = 1 * 10^3 kg/m^3

inner radius = 8.0 cm = 8 * 10 ^-2 m

outer radius = 9.0 cm = 9 * 10 ^-2 m

specific gravity = Density of liquid / density of water

Density of liquid = specific gravity * density of water = .80*1000 = 800 kg/m^3

V = (4 pi / 3) * (outer radius^3 * inner radius^3) = 9.09 *10 ^-4 m^3

weight of liquid = density of liquid * V * gravity = 7.127 N (buoyant force)

weight of sphere = weight of liquid + buoyant force = 7.127 + 7.127 = 14.254 N

mass of sphere = weight of sphere / gravity = 14.254/9.8 = 1.454 kg

density of sphere = mass of sphere / V = (1.454/(9.09 * 10^-4)) = 1.6 * 10^3 kg/m^3

-----All the work seems right, but I think the answer is not right. especially the calculation of the weight of the sphere. Can anybody help?

3. The attempt at a solution

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# Homework Help: Calculate the density of the material of which the sphere is made

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