A cube of ice 2 cm on a side is floating in a glass of water. You observe that the top of the ice is 0.166 cm above the surface of the water. What is the ratio of the density of ice to the density of water?

Question

anonymous · Answer

@JamesJ

badhi · Answer

Water volume replaced by the cube = (2-0.166)A cm (A is the cross sectional area of the cube)

Volume of the cube = 2A
According to the Archimedes law,
weight of the replaced water = weight of the ice cube
$$(2-0.166)A\rho_ig=2A\rho_wg$$

unit conversion is not necessary since its a ratio.