What is the mass of an object with a density of 12 g/ml and a volume of 3 ml?

Concept: Density is the amount of mass packed into each unit of volume of a substance, written ρ = m / V. Rearranging that defining relation gives mass = density × volume, so at a fixed density the mass of a sample is directly proportional to the volume it occupies.

Application

1. Read off the given quantities: density ρ = 12 g/ml and volume V = 3 ml.

2. Write the rearranged relation for the unknown: m = ρ × V.

3. Substitute the given values: m = 12 g/ml × 3 ml.

4. Multiply, letting ml cancel against ml, which leaves grams: m = 36 g.

Cross-check: Divide the result back by the volume: 36 g ÷ 3 ml = 12 g/ml, which is exactly the density stated in the question. The unit algebra agrees as well, since (g/ml) × ml leaves g, so the answer must come out in grams.

Where the other figures come from

• Adding gives 12 + 3 = 15, but a density and a volume are quantities of different kinds and cannot be added.

• Dividing gives 12 ÷ 3 = 4, and its units work out to g/ml2, not grams.

• Using a volume of 2 ml instead of the stated 3 ml gives 12 × 2 = 24 g.

Hence the mass of the object is 36 g.