Mark, a math enthusiast, loves creating tutorials because that stumped students and also those who must brush up on their math skills.

You are watching: How to find density with length, width and height and mass


Learn exactly how to calculation the density, mass, or volume that a hard object using this handy visual tool.


What Is Density?

Density is a measure up of exactly how compact (dense) things is. If an item has a greater density than water, the object will sink in water. If it has actually a lower thickness than water, it will float.

How do You job-related Out the density of a solid Object

To calculate an object's density, we'll require to know the object's mass and also volume. We deserve to then plug those values into the adhering to equation to calculation the object's density:

Density = massive / Volume

This formula is often written using the complying with symbols:

ρ: densitym: massV: volume

Using these icons as variables, our formula currently looks choose this:

ρ = m / V


The mass-density-volume triangle helps united state visualize the relationships between these 3 variables.


What Is the Density-Mass-Volume Triangle?

The density-mass-volume triangle (pictured above) is a visual tool that we deserve to use to figure out exactly how to calculate the density, mass, or volume of a solid object if we know the two continuing to be values. The triangle is divided into three parts, with thickness occupying the top part and mass and volume occupying the bottom 2 portions.

The location of each element of the triangle display us exactly how they relate to one one more through the formula over (Density = massive / Volume, or ρ = m / V).

How to calculation Density

If we want to calculate density, we merely cover up thickness in the triangle and see what remains. Because mass is over volume, we division mass through volume to gain density.

Density = mass / Volume

ρ = m / V

How to calculation Mass

If we desire to calculation mass, we simply cover increase mass in the triangle and also see what remains. Since density and volume are side by side, us multiply thickness by volume to get mass.

Mass = thickness * Volume

m = ρ * V

How to calculation Volume

If we want to calculate volume, we just cover up volume in the triangle and see what remains. Because mass is above density, we divide mass by thickness to obtain volume.

Volume = fixed / Density

V = m / ρ

Example troubles With Processes and Solutions

Let’s take it a look at some instance problems and also solve them using the density-mass-volume triangle described above.


In this an initial example, we must calculate the density of this rectangular prism, or cuboid.

Example 1

A solid rectangular box has actually a length of 6 cm, a width of 4 cm, and also a elevation of 5 cm. Job-related out the density of the box if the mass of package is 200 g.

This question asks us to job-related out the density. Therefore, we'll need the formula for thickness (Density = fixed / Volume).

However, the inquiry states the massive of the box but doesn’t state the volume, so we'll should work the end the volume of the box prior to we have the right to work the end the density.

Since the box is a cuboid, the volume have the right to be uncovered by multiply lengths that the 3 side lengths together:

Volume = size * broad * Height

V = 6 * 4 * 5

V = 120 cm³

Now the we have actually the volume, the density can be calculated:

Density = massive / Volume

ρ = m / V

ρ = 200 / 120

ρ = 1.67 g/cm³


In this 2nd example, we must calculate the mass of this triangle prism.

Example 2

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

This time, we space asked to work out the mass, so we'll require the formula for mass (Mass = thickness * Volume).

In this question, us are offered the density but not the volume, so let’s begin by calculating the volume that the triangle prism. The overcome sectional area that the prism have the right to be found by using the formula Area = ½ * (Base * Height).

A = ½ * (6 * 8) = 24 cm²

The volume the the prism deserve to now be discovered by multiply this area by the length:

ρ = 24 * 15

ρ = 360 cm³

Now that we have actually the volume, we can work out the massive of the triangle prism:

Mass = density * Volume

m = ρ * V

m = 3 * 360

m = 1080 g (or 1.08 kg)

This contents is accurate and also true to the finest of the author’s knowledge and also is not supposed to substitute for formal and individualized advice from a standard professional.

Questions & Answers

Question: A container is a rectangle-shaped prism. The dimensions space 50 centimeter X 40 centimeter X 10 cm. If it filled v water, what is the fixed of the water?

Answer: First, work-related out the volume that the rectangle-shaped prism by multiply the 3 dimensions together, 50 multiplied by 40 multiplied by 10 to give 20,000 cm^3. Now due to the fact that 1cm^3 is the very same as 1g of water the answer is 20,000g (or 20kg).

Question: how much fixed in rectangle-shaped prism height of 100 and also a size of 25 and width of 3?

Answer: an initial find the volume by multiplying the numbers with each other to give 7500. Now multiply this price by the thickness of the rectangular prism to provide the mass.

Question: exactly how do you calculate the thickness of a cube?

Answer: very first work the end the volume of the cube by cubing the side length.

Then division the massive (given in the question) by the volume.

Question: What is density?

Answer: thickness can be cleared up by dividing the massive by the volume.

See more: What Does It Mean When A Sketch Is Over Dimensioned? ? Ied Unit 3 Flashcards

Question: A wooden block is a rectangle-shaped prism. Its size is 8 cm, the length of one of the two perfect square sides is 2 cm, the mass of the wood block top top the electronic balance reads 150 grams, what is the density of the wood block?

Answer: very first work the end the volume of the block i beg your pardon is 32 cm^3 (8 times 2 time 2).