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Introduction to Solid Geometry

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Introduction to Solid Geometry
Density and Real-World Applications

18 min read

Density and Real-World Applications

Density connects a solid's mass to its volume, and is calculated using the volume formulas from this course.

Mass Per Volume

Term

$Density$

Exact definition

How tightly packed the material is — heavier materials have higher density for the same size.

In plain English

How tightly packed the material is — heavier materials have higher density for the same size.

Example

A metal with density 8 g /cm³ weighs 8 grams for every 1 cm³ of its volume.

Example 1 — finding mass from density and volume

A metal cube has side 5 cm and density 8 g /cm³. Find its mass. 1 Find the volume: 5^{3} = 125 cm³ 2 Use mass = density \times volume: 8 \times 125 Answer: 1000 g (1 kg)

Example 2 — finding density from mass and volume

A solid has mass 540 g and volume 60 cm³. Find its density. 1 Use density = mass \div volume: 540 \div 60 Answer: 9 g /cm³

Watch this mistake

Dividing the wrong way round

Calculating volume \div mass instead of mass \div volume when finding density.

Fix

Do this instead

Density is always mass \div volume — keep the formula's order fixed, and only rearrange it carefully when solving for a different unknown.

Practice

An object has mass 350 g and volume 50 cm³. Find its density.

Your answer

Take this with you

Before you go on

$Density = mass \div volume. Mass = density \times volume.$
$Finding a solid's volume (using the formulas from this course) is often the first step in a real density calculation.$

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More lessons in Introduction to Solid Geometry · Next: Scaling Solids · Previous: Composite Solids