Mass Volume Density Practice Problems and Review Worksheet Answers

Density Mass Volume

Density is a measure of how tightly the mass of an object is packed into the infinite it takes up. Information technology tin can be calculated by dividing mass by volume .

Make sure you are happy with the following topics before continuing.

• Rearranging Formulae
• Units and Conversions

Level four-five GCSE KS3

Density Mass Volume – Formula

Density , mass and volume are all related by the formula,

d = \dfrac{k}{Five}

where d is density , 5 is volume , and thou is mass . This can be rearranged in order to find book or mass depending on which quantities you lot are given and what the question asks y'all to find.

Mass is normally measured in grams, one thousand, or kilograms, kg, whereas, volume is normally measured in cubic centimetres, cm^iii, or cubic metres, m^3.

This means when dividing mass by volume, the resulting units are typically grams per cubic centimetre (g/cm^iii), or kilograms per cubic metre (kg/m^3). These are compound units (for more information, see conversions revision).

Level 4-5 GCSE KS3

Density Mass Book – Formula Triangle

A handy mode of remembering how to calculate either density , mass or volume  is to apply the triangles below.

The horizontal line means divide and the \times symbol means multiply.

We and so cover up the one we desire to detect (represented past a red circle) and comport out the adding with the other ii values from the triangle.

Level 4-v GCSE KS3

Case 1: Calculating Density

An object has a mass of 570 g and a volume of 2280 cm^3. Summate its density .

[2 marks]

Nosotros're looking for density, and then constructing the triangle and roofing d, we come across we must divide the mass by the volume. So

\text{density } = \dfrac{570}{2280} = 0.25 yard/cm^3

Level four-5 GCSE KS3

Example ii: Computing Mass

A cat has book 0.004 g^3 and density 980 kg/yard^three. Summate the mass of the cat.

[2 marks]

We're looking for mass, and so constructing the triangle and covering m, we see that to calculate the mass we must multiply the density by the volume. And then

\text{ Mass } = 980 \times 0.004 = 3.92 kg

Level 4-5 GCSE KS3

Example 3: Calculating Volume

A canteen of water has a density of yard kg/m^three and mass of 0.5 kg. Calculate the volume of the water bottle giving your reply in litres.

[2 marks]

We're looking for volume, then covering 5, nosotros must split the mass by the density. So

\text{ Volume } = \dfrac{0.5}{grand} = 0.0005 m^three

Multiplying this by 1000 to convert into litres, gives us the terminal answer,

\text{ Volume } = 0.5 50

Level 4-five GCSE KS3

Example Questions

We are calculating the volume, so by covering up the V nosotros can see from the triangle above that we have to dissever m by d.

Before we can exercise this, however, nosotros accept to brand certain that we have the correct units. The mass is in kilograms, just the density is in grams per cubic centimetre. This means that nosotros have to first catechumen the kilograms into grams earlier proceeding.

ii kg = 2000 one thousand

Therefore, the book of the olive oil can exist calculated every bit follows:

\text{Volume} = 2000 \div 0.925 = 2162cm^iii

We are calculating the  mass, so past roofing upward the m we can run across from the triangle to a higher place that we take to multiply d by V.

However, we don't know the volume, only we do know that the shape is a cube with a side length of 7 yard, so the volume of the cube is:

7 \times seven \times 7 = 343 m^3

Now that we know the volume, we tin multiply it by the density in order to summate the mass:

\text{Mass } = 343 \times 10,800,000 = 3,704,400,000 kg

To calculate the answer hither, we need to recall the formula:

\text{ density} = \text{ mass} \div \text{ volume}

In this question, the mass is 2460kg and the volume is 1.2 one thousand^3, so we just need to substitute these values into the formula as follows:

\text{ Density} = 2460 kg \div \, one.2 m^three = 2050 kg/thousand^3

a) In order to calculate the overall volume of the block, we demand to add the volume of metal A and the volume of metallic B.  Although we don't accept the volume of either metal, we have been given their masses and densities, so we can calculate the volume of each metal accordingly.

By rearranging the density formula, or using the triangle, we can work out how to calculate the volume:

\text{density} = \text{ mass}\div \text{ volume}

And then:

\text{volume} = \text{ mass}\div \text{ density}

The volume of metallic A tin be calculated as follows:

1200 g \div \, five g/cm^three = 240 cm^iii

The volume of metal B can be calculated every bit follows:

600 grand \div \, 3 one thousand/cm^3 = 200 cm^iii

Therefore, if metal A has a book of 240 cm^3 and B has a volume of 200 cm^3, then their combined volume is simply:

240 cm^3 + 200 cm^three = 440 cm^three

b) As we know from question a), the newly-formed cake has a book of 440 cm^3.

We know that the mass of metallic A was 1200 g and the mass of metal B was 600 g, so mass of the block is:

1200 grand + \, 600 g = 1800 chiliad

The density of this block tin be calculated by dividing the mass by the book every bit follows:

1800 g \div \, 440 cm^3 = 4.09 g/cm^3

This is quite a challenging question with a lot of calculations going on.

Since nosotros take been given the mass of metallic C and the ratio of metal A and metal B in metal C, nosotros can therefore summate the mass of metallic A and metallic B.  If the ratio of metal A to metal B is 3 : 7, that means that \frac{3}{ten} of the mass of metal C comes from metallic A and the remaining \frac{7}{10} is metallic B.  (We are dealing in tenths here since the sum of the ratio is 10.)

The mass of metal A can be calculated as follows:

2500 chiliad \times \dfrac{iii}{10} = 750 g

The mass of metal B can be calculated equally follows:

2500 g   \times \dfrac{7}{10} = 1750 thou

We at present know both the mass and density of both metals A and B, significant nosotros can piece of work out their respective volumes.

Since

\text{density} = \text{ mass} \div \text {volume}

so

\text{volume} = \text{ mass} \div \text {density}

The book of metal A can be calculated as follows:

750 g \div \, 3.ii g/cm^iii = 234.375 cm^3

The volume of metal A can exist calculated as follows:

1750 g \div \, 5.5 g/cm^iii = 318.18 cm^three

If metal A has a volume of 234.375 cm^three and metal B has a volume of 318.18 cm^3, then their combined volume is the volume of metal C.

Volume of metal C = 234.375 + 318.18 = 552.5568 cm^3

We now know both the mass and book of metal C, so we are now able to summate its density.

Density of metal C = 2500 g \div \, 552.5568 cm^3 = iv.5 g/cm^3

Related Topics

Worksheet and Instance Questions

Drill Questions

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