# Finding volume

This post introduces the concept of **volume**. Most of the activities are based around shapes made up of unit cubes such as centimetre cubes that are 1cm by 1cm by 1cm. This starts with the idea of 3D shapes building up in layers and then looks at some different contexts and interesting reverse problems. The topic is linked to number properties with a look at **cube numbers** and then there is a chance to consolidate learning with a set of cube and **cuboid** volume problems. At the end there are some other interesting related ideas for you to explore.

**Using layers to find volume**

In the first activity called **Layers** you should work out how many cubes there are in each of the 3D shapes shown. Try to use previous answers to help you.

In this last question, you may have used the same type of approach to work out the number of cubes even though you didn’t have the single layer shown first to start you off. The amount of space inside a shape is the **volume** of the **cuboid**.

Can you write down the volume of this final cuboid made up of centimetre cubes? The units of volume will be cm^{3}. How would you show how to calculate this volume from its dimensions? *Hint: in this case its dimensions are 4cm, 5cm and 10cm*.

**Volume in different contexts**

Try to think through and answer the problem on each slide in **Cube Buildings** from Don Steward:

In **Cut Away Volumes** eight identical blocks, 2cm by 3cm by 5cm, have each had a section cut away. The sections that have been removed all have **integer** dimensions. *Hint: an integer is a whole number.* The aim is to put them in order of size by volume.

**Using volume to find dimensions**

In the challenge task **Cuboidal parts** you need to work backwards from the volumes of cuboids to find their dimensions. This is a problem-solving activity that incorporates finding **factors** and **common** **factors**.

**Cube numbers**

In the final task there is another link to properties of number, with some slides to introducing **cube numbers** first:

On slide 3, use the visuals and the dimensions there to start you off, to work out and write down the 2nd, 3rd, 4th and 5th cube numbers. Note that 8 is the second cube number. These will be useful to complete the final task, where you should use the following visual prompts to calculate the **sum** of the **first five cube numbers**. Once you have the answer, the challenge is then to use the image underneath the cubes to demonstrate another number property that this answer has. *Hint: this time the image (made up of all of* *the small cubes above) shows a square rather than a cube.* *What are the dimensions of the square?*

**Volume of cube and cuboids**

Work through the problems on these slides from Teachit to consolidate all of this work on volume.

**Further ideas**

Watch the short clip from BBC Bitesize giving a rough idea of the history and development of the concept of area and volume from around the world here.

Or if you really want to blow your mind with ideas related to volume, topology and Klein Bottles, watch this Numberphile clip, *How to Fill a Klein Bottle*:

**ANSWERS – click below**

**Using layers to find volume**

200 cm^{3} = 4 cm x 5 cm x 10 cm

**Volume in different contexts**

**Using volume to find dimensions**

**Cube numbers**

The 2nd, 3rd, 4th and 5th cube numbers are 8, 27, 64 and 125.

The sum of the first five cube numbers is 1 + 8 + 27 + 64 + 125 = 225.

The image below shows that 225 = 15 x 15 = 15^{2}, or you could say in words that 225 is 15 squared.

**Volume of cubes and cuboids**

The version of the slides below will reveal the answers as you click through.