Density calculations

1. What is Mass?

Mass = how much matter an object has.

Key points

• It does not change with location (Earth, Moon, space).

• Different from weight (weight depends on gravity).

Units of Mass

• kilogram (kg) → SI unit

• gram (g)

• milligram (mg)

Conversions

• 1 kg = 1000 g

• 1 g = 1000 mg

Mass Calculation

Mass is usually measured using a balance, but it can also be calculated using density and volume​

2. What is Volume?

Volume = the amount of space an object occupies.

Units of Volume

• cubic meter (m³) → SI unit

• cubic centimeter (cm³)

• liter (L), milliliter (mL)

Conversions

• 1 m³ = 1000 L

• 1 L = 1000 mL

• 1 cm³ = 1 mL

Volume of Regular Solids

Cube V= a³

Cuboid V= l x b x h

Cylinder V=πr²h

4

Sphere V=​---- πr³

3

3. What is Density?

Density = mass per unit volume. It tells how compact or heavy something is for its size.

Volume

Density= ---------

Mass​

Units of Density

• kg/m³ → SI unit

• g/cm³ (very common in school problems)

Important Concept

• Higher density → object sinks

• Lower density → object floats

4. Density–Mass–Volume Triangle

This triangle helps you remember formulas:

Mass

   ----------

   Density | Volume

From the triangle:

• Mass = Density × Volume

• Density = Mass ÷ Volume

• Volume = Mass ÷ Density

Example Problems

Example 1: Find Density

Mass = 200 g Volume = 50 Mass cm³

                 200

Density= ------ = 4 g / cm³

                  50

Example 2: Find Mass

Density = 8 g/cm³ Volume = 10 cm³

Mass=8×10=80 g

Example 3: Find Volume

Mass = 540 g Density = 2 g/cm³

540

Volume = ------ =270 cm³

2

Floating & Sinking Rule

Object floats if:

Object density<Liquid density

Object sinks if:

Object density>Liquid density

Density of water = 1 g/cm³

Why is Density = Mass ÷ Volume?

1. What density actually means

Density tells us how much mass is packed into a given space.

In simple words, it means:

So density must compare:

• Mass → how much matter an object has

• Volume → how much space it occupies

This comparison is done using division, not multiplication.

2. Real-life example: Sponge vs Iron (same volume)

Imagine:

• 1 cm³ of sponge

• 1 cm³ of iron

They have the same volume, but:

• Sponge has very little mass

• Iron has much more mass

So the question becomes:

That idea is written as: Mass Density = -------- Why is Density = Mass ÷ Volume?

1. What density actually means

Density tells us how much mass is packed into a given space.

In simple words, it means:

So density must compare:

• Mass → how much matter an object has

• Volume → how much space it occupies

This comparison is done using division, not multiplication.

2. Real-life example: Sponge vs Iron (same volume)

Imagine:

• 1 cm³ of sponge

• 1 cm³ of iron

They have the same volume, but:

• Sponge has very little mass

• Iron has much more mass

So the question becomes:

That idea is written as:

Mass

Density = ----------

Volume

3. Why not Mass × Volume?

If we multiplied mass and volume:

• Bigger objects would automatically seem denser

• This gives incorrect physical meaning

Example:

• A balloon has a very large volume but very small mass

• Multiplication would give a large value, which is misleading

Division removes the effect of size and shows how tightly matter is packed.

4. Mathematical logic

If:

• Volume stays the same

• Mass increases

Then density should increase.Division shows this correctly.

If:

• Mass stays the same

• Volume increases

Then density should decrease. Division again gives the correct result.

5. Scientific definition

   Scientists defined density as:

   Mass per unit volume

The word “per” always means division.

Examples:

• Speed = distance per time

• Pressure = force per area

• Density = mass per volume

  6. One-line

Density is defined as mass per unit volume, therefore density equals mass divided by volume.