How To Find Volume With Density And Mass Given

Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to castor up on their math skills.

Learn 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 meaty (dumbo) an object is. If an object has a greater density than h2o, the object volition sink in h2o. If information technology has a lower density than h2o, it volition bladder.

How Do You Work Out the Density of a Solid Object

To calculate an object's density, we'll need to know the object's mass and volume. Nosotros can then plug those values into the post-obit equation to calculate the object'due south density:

Density = Mass / Volume

This formula is oft written using the post-obit symbols:

ρ: density
m: mass
V: book

Using these symbols as variables, our formula at present looks like this:

ρ = g / V

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

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What Is the Density-Mass-Volume Triangle?

The density-mass-volume triangle (pictured to a higher place) is a visual tool that we can use to figure out how to calculate the density, mass, or volume of a solid object if nosotros know the 2 remaining values. The triangle is divided into three parts, with density occupying the acme portion and mass and volume occupying the bottom 2 portions.

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

How to Calculate Density

If nosotros want to calculate density, we only embrace up density in the triangle and meet what remains. Since mass is above volume, nosotros divide mass by volume to go density.

Density = Mass / Volume

ρ = m / V

How to Calculate Mass

If we desire to summate mass, we simply cover upwardly mass in the triangle and see what remains. Since density and volume are side by side, we multiply density by volume to go mass.

Mass = Density * Volume

m = ρ * 5

Example Problems With Processes and Solutions

Let'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 get-go instance, 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 4 cm, and a pinnacle of five cm. Work out the density of the box if the mass of the box is 200 chiliad.

This question asks us to piece of work out the density. Therefore, we'll need the formula for density (Density = Mass / Volume).

However, the question states the mass of the box just doesn't land the book, so we'll need to work out the volume of the box before we tin 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 * Top

V = 6 * 4 * 5

V = 120 cm³

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

Density = Mass / Volume

ρ = one thousand / V

ρ = 200 / 120

ρ = 1.67 grand/cm³

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

Case ii

Work out the mass of this triangular prism if the density is iii one thousand/cm³.

This time, we are asked to piece of work out the mass, so we'll demand the formula for mass (Mass = Density * Volume).

In this question, nosotros are given the density just not the volume, so let's begin by calculating the book of the triangular prism. The cross sectional surface area of the prism tin be found by using the formula Area = ½ * (Base * Height).

A = ½ * (6 * 8) = 24 cm²

The book of the prism can now be found by multiplying this expanse past the length:

ρ = 24 * xv

ρ = 360 cm³

Now that nosotros accept the book, we can work out the mass of the triangular prism:

Mass = Density * Volume

k = ρ * 5

m = iii * 360

k = 1080 yard (or 1.08 kg)

This content is accurate and true to the best of the author's knowledge 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 50 cm X 40 cm X 10 cm. If it filled with water, what is the mass of the water?

Answer: Outset, work out the volume of the rectangular prism by multiplying the three dimensions together, 50 multiplied past 40 multiplied by 10 to requite 20,000 cm^3. Now since 1cm^iii is the same as 1g of h2o the answer is twenty,000g (or 20kg).

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

Respond: Get-go notice the volume by multiplying the numbers together to give 7500. Now multiply this answer by the density of the rectangular prism to give the mass.

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

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

Then divide the mass (given in the question) by the volume.

Question: What is density?

Answer: Density can be worked out by dividing the mass by the book.

Question: A wooden cake is a rectangular prism. Its length is 8 cm, the length of 1 of the two perfect square sides is 2 cm, the mass of the wooden cake on the electronic balance reads 150 grams, what is the density of the wooden cake?

Answer: Outset work out the volume of the cake which is 32 cm^3 (viii times two times ii).

And so divide 150 by 32 to give 4.6875 yard/cm^iii