Question

A rectangular box 4 meters long, 3 meters wide and 2 meters tall. On the box is a cat, and the box is floating in water such that half the box is under water. The density of the box is 300 kg/m³. What is the mass of the cat?

Answer 1

Mass of the cat = 16800kg

Explanation:

The volume of the box = its length * its breath * its height- 4m × 3m × 2m = 24
`m^(3)`

The standard density of water is 1000 Kg/
`m^(3)`

By Archimedes principle, the mass of a body floating body is equivalent to the mass of the volume liquid displaced

in this case we have

Mass of water displaced = Density of the water × Volume of the water displaced = 1000 Kg/
`m^(3)` × 24
`m^(3)` = 24000kg

The mass of the box = Box density × Box volume = 24
`m^(3)` × 300kg/
`m^(3)` = 7200 kg Hence the mass of water displaced = mass of the foating box + mass of th cat

24000kg = mass of cat +7200kg

mass of cat = 24000kg - 7200kg = 16800kg