According to Archimedes' principle, the mass of a floating object equals the mass of the fluid displaced by the object. Use this principle to solve the following problems.
(a) A wooden cylinder 30.0 cm high floats vertically in a tub of water (density = 1:00 g/cm3). The top of the cylinder is 13.5 cm above the surface of the liquid. What is the density of the wood?
(b) The same cylinder floats vertically in a liquid of unknown density. The top of the cylinder is 18.9 cm above the surface of the liquid. What is the liquid density?
(c) Explain why knowing the length and width of the wooden objects is unnecessary in solving Parts (a) and (b).