Question

A piece of lead has the shape of a hockey puck, with a diameter of 7.5 cm and a height of 2.4 cm. If the puck is placed in a mercury bath, it floats.

Part A

How deep below the surface of the mercury is the bottom of the lead puck?

Express your answer using two significant figures.

Answer 1

density of mercury is 13.55 g/cc
density of lead is 11.34 g/cc

the weight of the displaced mercury equals the weight of the lead puck
the 'hole' in the mercury has the same shape as the lead puck, of course
so the only difference will be in the heights of the 'hole' and the puck
and the masses/weights are proportional to volumes

from D = m/V
m = D V = D (A h) {{V - base area x height}}
masses are equal so
(D A h) mercury = (D A h) lead
A's are equal so cancel
13.55 h = 11.34 (2.4)
h = 2.0 cm to two sig figs