The Density, Mass and Volume Magic Triangle: How to Calculate Density of a Solid Shape

The density, mass and volume triangle is as follows:

So if you wanted to work out the density, you would cover up density in the magic triangle to give:

Density = Mass/Volume

(since mass is above volume)

So if you wanted to work out the mass, you would cover up mass in the magic triangle to give:

Mass = Density × Volume

(since density and volume are side by side)

And if you wanted to work out the volume, you would cover up volume in the triangle to give:

Volume = Mass/Density

(since mass is over density in the triangle)

Density basically tells you how compact an object is. If an object has a greater density than water the object will sink and it will float if the object has a lower density than water.

Let’s take a look at a some examples of using this density, mass and volume triangle.

Example 1

A solid rectangular box has a length of 6 cm, a width of 4 cm and a height of 5cm. Work out the density of the box if the mass of the box is 200g.

So the question ask you to work out the density. Therefore, you need the formula for density (Density = Mass/Volume).

However, the question states the mass of the box but doesn’t state the volume. So you need to work out the volume of the box before you can work out the density.

Since the box is a cuboid, the volume of the cuboid can be found by multiplying the three side lengths together:

Volume of cuboid = Length × Width × Height

= 6 × 4 × 5

= 120 cm³

Since you now have the volume the density can be calculated:

Density = Mass/Volume

= 200/120

= 1.67 g/cm³

Example 2

Work out the mass of this triangular prism if the density is 3 g/cm³.

This time you are asked to work out the mass so you need the formula:

Mass = Density × Volume

In the question you are given the density but not the volume again. So let’s begin by calculating the volume of the triangular prism.

The cross sectional area of the prism can be found by using the formula 1/2bh:

Area of triangle = ½ × 6 × 8 = 24cm²

So the volume of the prism can now be found by multiplying this area by the length:

Volume of prism = 24 × 15 = 360 cm³

Since the volume is now found you can finally work out the mass of the triangular prism:

Mass = Density × Volume

= 3 × 360

= 1080g or 1.08kg

For some extra questions on working with density try the link below:

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