# Functional Skills: Volume

## Functional Skills: Volume Revision

**Volume of 3D Shapes**

The **volume** of an object is how much space it takes up. Volume involves lengths being multiplied 3 times â€“ so the units for length need to be multiplied together 3 times too. Therefore, we get units like metres cubed (m^3), centimetres cubed (cm^3) and millimetres cubed (mm^3) for volume.

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

**Volume of Cubes and Cuboids**

The volume of a cuboid is given by:

\text{Volume of cuboid} = \textcolor{blue}{\text{length} \times \text{width} \times \text{height} = l \times w \times h}

For a cube, all sides are the same length, so the volume of a cube is given by:

\text{Volume of cube} = \textcolor{blue}{\text{length} \times \text{length} \times \text{length} = l \times l \times l = l^3}

## Follow Our Socials

Our Facebook page can put you in touch with other students of your course for revision and community support. Alternatively, you can find us on Instagram or TikTok where we're always sharing revision tips for all our courses.

**Volume of Prisms and Cylinders**

The volume of a prism is given by:

\text{Volume of prism} = \textcolor{red}{\text{cross-sectional area}} \times \textcolor{limegreen}{\text{length}}

This is the case for **any prism**, including cubes and cuboids. The **cross-sectional area** on a prism is the area of the front or back face. For a triangular prism, the cross-sectional area is a triangle and for a cylinder (which is like a prism) it is a circle.

So, the volume of a cylinder is given by

\text{Volume of cylinder} = \textcolor{red}{\pi r^2} \times \textcolor{limegreen}{\text{length}}

**Example 1: Volume of a Cuboid**

Below is a rectangle. The rectangle has a length of 18 cm, a width of 8 cm and a height of 5 cm.

Calculate the volume of the cuboid.

**[2 marks]**

We need to multiply the length by the width by the height.

\text{Volume} = \text{length} \times \text{width} \times \text{height} = 18 \times 8 \times 5 = 720 cm^3

**Example 2: Volume of a Prism**

Below is a triangular prism. The triangular face has base of 6\text{ cm} and height of 5\text{ cm}. The length of the prism is 3.5\text{ cm}.

Calculate the volume of this prism.

**[3 marks]**

The first step in this question is to work out the area of the cross-section, so the triangle.

We can do this as follows,

\dfrac{1}{2}(6\times5)=15\text{ cm}^2

The next step is to multiply the cross-sectional area by the length of the prism,

Â \text{Volume} = 15\times3.5=52.5\text{ cm}^3

## Functional Skills: Volume Example Questions

**Question 1:Â **The diagram below shows the outline of a cuboid, ABCDEFGH, with dimensions: AB=3 cm, BC=12 cm, and CF=16 cm.

Calculate the volume of the cuboid.

**[2 marks]**

Multiply the length by the height by the width:

Volume = 3\times12 \times16=576 cm^3

**Question 2:** Calculate the volume of a cube of sides of length 5 cm.

**[2 marks]**

The volume of a cube is calculated by cubing the length of one of its sides:

Volume = 5 \times 5 \times 5 = 125 cm^3

**Question 3:** A cylinder has a diameter of 8 cm and a length of 5 cm.

Find the volume of the cylinder, giving your answer to the nearest whole number.

Use \pi = 3.14

**[3 marks]**

Radius = 8 \div 2 = 4 cm

Area of circle = \pi r^2 = 3.14 \times 4^2 = 50.24 cm^2

Volume = 50.24 \times 5 = 251.2 = 251 cm^3 (nearest whole number)

## Functional Skills: Volume Worksheet and Example Questions

### Volume L1

FS Level 1NewOfficial PFS### Volume L2

FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]

## Revision Products

### Functional Skills Maths Level 2 Pocket Revision Guide

Revise and practice for your functional skills maths level 2 exam. All topics covered in this compact revision guide.

### Functional Skills Maths Level 2 Mini Tests

Practice for your functional skills Maths level 2, questions from every topic included.

### Functional Skills Maths Level 2 Revision Cards

Revise for functional skills maths level 2 easily and whenever and wherever you need. Covering all the topics, with revision, questions and answers for every topic.

### Functional Skills Maths Level 2 Practice Papers

This 5 set of Functional Skills Maths Level 2 practice papers are a great way to revise for your Functional Skills Maths Level 2 exam. These practice papers have been specially tailored to match the format, structure, and question types used by each of the main exam boards for functional skills Maths. Each of the 5 papers also comes with a comprehensive mark scheme, so you can see how well you did, and identify areas to improve on.

### Functional Skills Maths Level 2 Practice Papers & Revision Cards

This great value bundle enables you to get 5 functional skills maths level 2 practice papers along with the increasingly popular flashcard set that covers the level 2 content in quick fire format.