How to find the volume of shapes is another maths that students can find a bit tricky at the beginning. Usually, perimeter and area are taught first, with how to find the volume of shapes to follow. These three maths topics are under the same umbrella, so to speak. The hardest part is remembering which is which! But practice makes perfect so the more how to find the area perimeter and volume of shapes questions that your child does, the easier it will be to remember the difference. Volume is more likely to start appearing in your child’s homework during Primary 6, and it will come up in their transfer test preparation. So let’s get started learning all about the volume of shapes!
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How to find volume of a shape
The volume of a shape is how much space a 3D shape takes up. Volume is the 3D shape equivalent to the area of a 2D shape. Students can be asked how to find the volume of a shape 3D, or it can appear in word problem format. Some of the word problems which contain volume can be a bit challenging, but don’t worry, we are going to go through everything that your child needs to know about volume!
What is the difference between volume, area and perimeter?
Volume, area and perimeter are under the same umbrella when it comes to maths topics. Area and perimeter are usually taught first, with volume being taught a bit later on in primary school. So, what are the differences between all three of these maths concepts?
The perimeter of a shape is the total distance around the outside of a shape. The area of a shape measures the inside of a 2D shape. The volume of a shape measures the inside of a 3D shape. However, the major difference between area and volume is that area is for 2D shapes and volume is for 3D shapes.
What is a 3D shape?
Volume is only used with 3D shapes, but what is a 3D shape? 3D stands for three-dimensional, and this is a solid shape which you can hold in your hand. The difference between a 3D shape and a 2D shape is that 3D shapes are solid, you can hold them in your hand, whereas a 2D shape is flat and have no thickness or height. Some examples of 3D shapes are a cube, cuboid, pyramid, cylinder and cone.
How to find volume of shapes
To calculate the volume of a shape, we multiply the length by the height by the width. With volume, we will be multiplying three numbers. For example, if the measurements of a 3D shape are 5m, 6m and 5m, we will calculate 5 x 6 = 30. We will then calculate 30 x 5 = 150. The volume of the shape is 150m3. The units of measurement for volume will always have the cubed symbol after the metric unit. With this example, the metric unit is metres, the unit will be m3.
Volume and missing measurements
Finding the volume of a basic 3D shape is the most common form of volume question. However, some tricky ones can be thrown into your child’s homework or transfer test preparation to try and catch them out! One of those types of questions is finding the volume of a 3D shape when there is a missing measurement. There are two ways that this type of question can be asked. The first is finding the missing measurement of a shape when the volume is given. The second is using the area of a 3D shape’s face to find the volume. Let’s take a look at each type.
Finding the missing measurement of a shape when the volume is given:
This type of question is one that I have seen come up in transfer test revision materials and practice papers in the past. Students are given the volume of a shape alongside two measurements. The question will ask them to find the missing measurement in the shape. The missing measurement could be the length, height or width.
For example, the volume of the cuboid below is 240cm3. What is the value of the missing width of the cuboid? We are given the length and height of the shape in the question. The length is 10cm and the height is 6cm. To find the missing width, we must first multiply 10 by 6, which gives us 60cm. We will then take the total volume and divide it by 60 to find the missing width of the cuboid. 240 divided by 60 gives us 4. The missing width of the cuboid is 4cm!
Using area to find the volume of a shape:
This type of question is going to be asked using only a cube. The reason for this is that all sides of the cube are the same. Initially, the question will appear to be super challenging, but if you take a minute and remember that all the measurements will be the same, then it’s not too bad.
For example, one face of a cube has an area of 36cm2. What is the volume of the cube? We know that all the measurements of the cube are the same; this means the number that we multiply to get 36cm has to be the same. If we multiply 6 by 6, we get 36. This means the third measurement that we need to find the volume of the cube is also 6cm. To find the volume of the cube, we multiply 6 by 6 by 6! This gives us an answer of 216cm3.
Volume Word Problems
Volume word problems can come up in a lot of different ways. Some are more direct and ask you to find the volume, and others don’t directly ask students how to get volume of a shape, but that is what’s required to get the answer to the word problem. With these types of word problems, students need to use the clues in the question to realise that volume is being asked. I always say this when it comes to word problems, but I’ll say it again. Remember, word problems are a mathematical calculation with a story around them. If no shape graphics are included with the word problem, your child can draw one out quickly as part of their working out, if it helps them to visually see the shape.
I am going to go through two examples with you of how to find volume of shapes can be asked in a word problem. Example 1 will be when finding the volume is asked directly, and Example 2 will be when it is not so obvious.
Example 1:
Sandra bought a new suitcase for her holidays. The length, height and width of her suitcase are 8m, 3m and 4m. What is the volume of Sandra’s new suitcase? With this volume word problem, there is no shape graphic included, but we know that we are supposed to find the volume because it is specifically asked in the word problem.
To find the volume of Sandra’s suitcase, we will multiply 8 by 3, which gives us 24. We will then multiply 24 by 4, which gives us 96. The volume of Sandra’s suitcase is 96m3.
Example 2:
A large box is used to store smaller boxes of biscuits. How many small boxes will fit into one large box? With this word problem, we are not specifically asked to find the volume of the boxes. However, this is what we need to do to find out how many smaller boxes will fit into the large box. This type of question can come up in transfer test preparation and practice papers, so be on the lookout for them.
To find the answer to this question, we need to find the volume of the larger box by multiplying 8 by 5 by 4. This gives us a volume of 160cm3. Then we need to find the volume of the smaller box by multiplying 4 by 2 by 1. This gives us a volume of 8cm3. The last step of this question is to divide the volume of the large box by the volume of the smaller box to find out how many will fit inside. 160 divided by 8 gives us 20. So 20 small boxes will fit into the large box.
Volume of Compound Shapes
These types of volume questions can make students freak out when they first see them. They look so complicated and confusing. But just like finding the area of a compound shape, we need to take it step by step. How to find volume of irregular solids or compound shapes isn’t something that your child will come across in their transfer test preparation, but you never know if it will pop up, so it’s better to go over it to be sure. Let’s take a look at an example together.
Step 1: Split or Divide the Shape
The first thing that we need to do when we see a compound shape is not to panic! Splitting or dividing the shape into two or more manageable shapes will make the question easier, rather than wondering how to find volume of two shapes straight away! Sometimes the shape will be already clearly divided, and sometimes it won’t be.
Step 2: Compound Shapes Volume
Once the shape has been split up into more manageable shapes, we are going to find the volume of each of the shapes separately. Remember to find the volume, we are multiplying the height by the length by the width.
Step 3: Add
Once we have found the volume of each of the separate shapes, it’s time to add them all together to find the volume of the complete shape. And that’s it! We’ve just found the volume of a compound shape.
Volume Transfer Test Questions
How to find volume KS2 is a maths topic that has come up time and time again over the years. Just like with area and perimeter, there are several ways that your child can be asked to demonstrate their knowledge of how to find out the volume of a shape in the transfer test, so your child must be confident with them all. The volume questions that I have seen come up in the transfer test in the past are:
- Volume of 3D shapes
- Volume of shapes with missing lengths
- Volume word problems
Let’s go through a SEAG transfer test style volume question for each of these ways so you can help your child with them when they come up during their transfer test preparation.
Volume of 3D Shapes
The first and easiest way that volume can be asked in the transfer test is how to find the volume of a shape 3D. Usually, it will be a cube or cuboid. The question will specifically ask students to find the volume of a shape. To do this we multiply the height, by the length, by the width. For example, what is the volume of the cuboid below?
Volume of shapes with missing measurements
Another example is using volume to find missing measurements from a shape. This is when volume starts to get a little bit trickier at first. But it’s easy when you know how! With these types of questions, we need to use the information we have been given in the question to find the missing measurements. For example, Cube A and Cuboid B have the same volume. What is the missing length from Cube A?
Volume word problems
It wouldn’t be the transfer test if some sneaky word problems weren’t thrown in. When it comes to word problems, always remind your child that word problems are just a mathematical calculation with a ‘story’ around them. For example, Tina got a new jewellery box as one of her birthday presents. The box measures 12cm wide, 7cm in height and 6cm in length. What is the volume of her jewellery box? If we take out the ‘story’ of Tina’s birthday and her present, we are left with a mathematical calculation. Multiply 12 by 7 by 6 to find the volume.
Here is another example of a volume word problem that is transfer test style. Marty buys an apartment in France. He needs to fill the swimming pool with water. The swimming pool measures 40m by 20m by 15m. How much water does Marty need to fill the pool? This question does not specifically ask you to find the volume, but that is exactly what we need to do. When we multiply 40 by 20 by 15, this will tell us how much water Marty needs to fill the pool.
More information on how to find volume of shapes
Fun and Easy Activities for Practicing Volume
Teach your child how to find the area of shapes and make homework time easy!
How to find the area perimeter and volume of different shapes are three maths topics that your child will be working with throughout their maths lessons for years to come. Building a solid foundation and understanding of these topics now in primary school will help them be better prepared for sitting the transfer test and for secondary school. Make sure you check out my blog posts on perimeter and area if your child needs a bit of help with these. And if your child ever gets confused with volume, come right back to this blog post, and I will help you out with how to find volume of shapes!
