Density Chemistry Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A solid cube has a side length of 3.0 cm3.0 \text{ cm} and a mass of 81 g81 \text{ g}. Calculate its density. If the cube is cut in half, what is the density of each piece? Explain.

Solution

  1. 1
    Volume of cube: V=s3=(3.0)3=27 cm3V = s^3 = (3.0)^3 = 27 \text{ cm}^3.
  2. 2
    Density: ρ=mV=8127=3.0 g/cm3\rho = \frac{m}{V} = \frac{81}{27} = 3.0 \text{ g/cm}^3.
  3. 3
    When cut in half, each piece has half the mass (40.5 g40.5 \text{ g}) and half the volume (13.5 cm313.5 \text{ cm}^3). Density = 40.513.5=3.0 g/cm3\frac{40.5}{13.5} = 3.0 \text{ g/cm}^3 — unchanged.

Answer

ρ=3.0 g/cm3 for both the whole cube and each half.\rho = 3.0 \text{ g/cm}^3 \text{ for both the whole cube and each half.}
Density is an intensive property — it does not depend on the amount of material. Cutting an object changes its mass and volume proportionally, so the ratio stays the same.

About Density

The mass of a substance per unit volume, measuring how tightly packed the particles are within a material.

Learn more about Density →

More Density Examples

Example 1 easy

A block of aluminum has a mass of [formula] g and a volume of [formula]. Calculate its density.

Example 2 medium

A piece of metal has a mass of [formula] g. When placed in a graduated cylinder containing [formula]

Example 3 easy

Will an object with density [formula] float or sink in water ([formula])?

← All Density Examples Density Concept