Question

A graduated cylinder is filled with 20ml of water. Then, an 8g marble is dropped into the cylinder, causing the volume to change to 24ml. What is the density of the marble?

Answer 1

The density of the marble is 2,000 kg/m³

Explanation:

The given parameters for finding the density of the marble are;

The volume of water in the graduated cylinder, v₁ = 20 ml

The mass of the marble dropped into the graduated cylinder, m = 8 g

The new volume of the cylinder after the 8 g marble is dropped into the cylinder, v₂ = 24 ml

Therefore, the volume of the marble, v = v₂ - v₁

Substituting the known values gives;

The volume of the marble, v = 24 ml - 20 ml = 4 ml

Density, ρ = Mass, m/(Volume, v), the units of density is kg/m³

Therefore, the density of the marble,
`\rho _(marble)`, is given as follows;

`\rho _(marble)` = m/v = (8 g)/(4 ml) = 2 g/ml

1 g/ml = 1 kg/l = 1,000 kg/m³

∴
`\rho _(marble)` = 2 kg/l = 2,000 kg/m³.