How To Find Volume Using Density

Mark, a math enthusiast, loves writing tutorials for stumped students and those who demand to brush upwards on their math skills.

Learn how to calculate the density, mass, or volume of a solid object using this handy visual tool. — Larn how to calculate the density, mass, or volume of a solid object using this handy visual tool.

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What Is Density?

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

How Do You Work Out the Density of a Solid Object

To calculate an object's density, we'll need to know the object'south mass and volume. We can then plug those values into the following equation to calculate the object'southward density:

Density = Mass / Volume

This formula is often written using the following symbols:

ρ: density
m: mass
V: book

Using these symbols equally variables, our formula now looks like this:

ρ = m / V

The mass-density-volume triangle helps us visualize the relationships between these three variables. — The mass-density-volume triangle helps the states visualize the relationships between these three variables.

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What Is the Density-Mass-Book Triangle?

The density-mass-book triangle (pictured above) is a visual tool that we tin can use to figure out how to calculate the density, mass, or book of a solid object if nosotros know the two remaining values. The triangle is divided into three parts, with density occupying the top portion and mass and volume occupying the bottom two portions.

The positions of each element of the triangle show the states how they chronicle to one another through the formula above (Density = Mass / Volume, or ρ = m / V).

How to Calculate Density

If we want to summate density, nosotros simply cover up density in the triangle and see what remains. Since mass is to a higher place volume, nosotros separate mass by book to become density.

Density = Mass / Book

ρ = thou / V

How to Summate Mass

If nosotros want to calculate mass, we simply cover up mass in the triangle and encounter what remains. Since density and volume are side by side, we multiply density past volume to go mass.

Mass = Density * Volume

thousand = ρ * V

Instance Problems With Processes and Solutions

Permit's take a look at some instance problems and solve them using the density-mass-volume triangle explained above.

In this first example, we need to calculate the density of this rectangular prism, or cuboid. — In this first example, nosotros need to calculate the density of this rectangular prism, or cuboid.

Example 1

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

This question asks u.s.a. to work out the density. Therefore, we'll demand the formula for density (Density = Mass / Volume).

Notwithstanding, the question states the mass of the box but doesn't land the volume, and so we'll need to work out the book of the box before nosotros can work out the density.

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

Volume = Length * Width * Height

V = half dozen * 4 * 5

V = 120 cm³

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

Density = Mass / Volume

ρ = g / V

ρ = 200 / 120

ρ = 1.67 g/cm³

In this second example, we need to calculate the mass of this triangular prism.

Example 2

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

This time, we are asked to work out the mass, so we'll need the formula for mass (Mass = Density * Book).

In this question, we are given the density but not the volume, so let's begin by calculating the volume of the triangular prism. The cross sectional area of the prism can exist found by using the formula Area = ½ * (Base * Height).

A = ½ * (6 * 8) = 24 cm²

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

ρ = 24 * 15

ρ = 360 cm³

At present that we have the volume, we can work out the mass of the triangular prism:

Mass = Density * Book

m = ρ * Five

grand = 3 * 360

m = 1080 thou (or 1.08 kg)

This content is accurate and true to the best of the author'south cognition and is not meant to substitute for formal and individualized advice from a qualified professional.

Questions & Answers

Question: A container is a rectangular prism. Its dimensions are l cm X 40 cm Ten ten cm. If it filled with water, what is the mass of the h2o?

Answer: Kickoff, work out the volume of the rectangular prism past multiplying the three dimensions together, l multiplied by 40 multiplied by x to give 20,000 cm^iii. Now since 1cm^iii is the same as 1g of water the answer is 20,000g (or 20kg).

Question: How much mass in rectangular prism height of 100 and a length of 25 and width of 3?

Answer: First find the book by multiplying the numbers together to give 7500. Now multiply this respond past the density of the rectangular prism to give the mass.

Question: How do you summate the density of a cube?

Answer: First work out the volume of the cube by cubing the side length.

And so carve up the mass (given in the question) by the volume.

Question: What is density?

Respond: Density can be worked out past dividing the mass by the volume.

Question: A wooden block is a rectangular prism. Its length is viii cm, the length of one of the two perfect square sides is ii cm, the mass of the wooden block on the electronic balance reads 150 grams, what is the density of the wooden block?

Respond: First work out the volume of the block which is 32 cm^3 (viii times ii times 2).

Then divide 150 by 32 to give iv.6875 thousand/cm^3