What is a volume? The word usually refers to the amount of three-dimensional space that an object occupies. It is commonly measured in cubic centimetres (cm3) or cubic metres (m3).

A closely related idea is capacity; this is used to specify the volume of liquid or gas that a container can actually hold. You might refer to the volume of a brick and the capacity of a jug â€“ but not vice versa. Note that a container with a particular volume will not nec
Author(s): The Open University

## Question 1

Find the area of a circle of (a) radius 8 cm, and (b) radius 15 m.

• (a)

Author(s): The Open University

## Question 1

Find the area of each of these shapes.

Author(s): The Open University

## Question 1

Calculate all the angles at the centres of these objects.

Here is an improved solution which shows working.

## Example 13

Suppose you plan to redecorate your bathroom. The end wall has the following shape, with dimensions as shown on the diagram. The quality of the plasterwork is not good and you are considering tiling the wall.

Author(s): The Open University

In this type of question you are given the answer! All the marks are allocated for correct reasoning and justification.

## Example 15

Suppose you now decide to place your new bath (length 1.7 m, height 0.8 m) against this wall as shown in the diagram below.

Author(s): The Open University

Consider some of the many different things we can do with language: express ourselves in metaphor, issue commands, ask questions, fill in crosswords, write shopping lists and diary entries, repeat nursery rhymes by rote, solve logical or arithmetical problems, make promises, tell stories, sign our names, etc. Impressive though it is, this variety in the uses of language is a potential distraction from our main interest, which is in the use of language to represent. It will therefore help if w
Author(s): The Open University

Section 6 contains solutions to the exercises that appear throughout sections 1-5.

Click the link below to open the solutions (13 pages, 232KB).

Section 6

Author(s): The Open University

Fractions and decimals can also be converted to percentages, by multiplying by 100%.

So, for example, 0.17, 0.3 and can be expressed as percentages as follows:

Â Â 0.17 Ã— 100% = 17%;

<
Author(s): The Open University

Ratios crop up often in official statistics. The government wants the teacherâ€“pupil ratio in schools to be increased to one teacher to thirty pupils or less. The birth rate has fallen: the ratio of children to women of child bearing age has gone down. It used to be 2.4 to 1, and now it is 1.9 to 1. Predictions for the ratio of working adults to retired adults is disturbing. Predictions are, that by 2030 the ratio will be two working adults to every retired person, instead of three to one no
Author(s): The Open University

The content acknowledged below is Proprietary (see and conditions made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence) and used under licence.

Course image: rod
Author(s): The Open University

Mathematical processes are different from content in that they overarch the subject and are not thought of as hierarchical. A list of processes could contain:

• problem-solving (including investigating);

• mathematical modelling;

• reasoning;

• communicating;

• making connections (including applying mathematics); and

• using tools.

Each of the six processes listed here repre
Author(s): The Open University

World in transition: Managing Resources
Do you take your access to water for granted? The Peruvian and Tanzanian communities featured in this album certainly donâ€™t. This album examines how development agencies can empower communities to help themselves by introducing simple technologies, and facilitate the sharing of ideas through education. In the Andean mountains, scarce supplies of water and agricultural challenges give rise to conflict; but the changes engineered by development agencies can start to show a way out of poverty. Me
Author(s): The OpenLearn team

Environment: habitat and conservation
The relationship between sea and land has always been one of dynamic change. Yet, as rising sea levels threaten habitats for wildlife and humans alike, we are today more vulnerable than ever. The 11 video tracks on this album address the complexities of environmental change, focusing on the Blackwater Water Estuary in Essex where a coastal retreat scheme is in operation, managed biodiversity at Wicken Fen in Cambridgeshire, and the search for sustainable forms of development along the River Seve
Author(s): The OpenLearn team

War, Intervention and Development
How can we prevent a country from returning to civil war? When and how should external parties intervene in serious conflicts? This album looks at the decade of violence and destruction that occurred in Sierra Leone in the 1990's. Now that peace has finally come about through the efforts of the international community, it's time to debate whether the root causes of war have been adequately addressed, and what lessons can be learned. 50% of Sierra Leoneans are under 15 and unskilled. Lack of edu
Author(s): The OpenLearn team

Understanding the environment: Learning and communication
There is increasing recognition that the reductionist mindset that is currently dominating society, rooted in unlimited economic growth unperceptive to its social and environmental impact, cannot resolve the converging environmental, social and economic crises we now face. The primary aim of this free course, Understanding the environment: Learning and communication, is to encourage the shift away from reductionist and human centred thinking towards a holistic and ecological worldview.
Author(s): Creator not set

Introducing the environment: Ecology and ecosystems
What is ecology and why is it important to our understanding of the world around us? This free course, Introducing the environment: Ecology and ecosystems, looks at how we can study ecosystems to explore the effect that humans are having on the environment. First published on Fri, 18 Mar 2016 as Author(s): Creator not set

Water for life
Atoms, elements and molecules are the building blocks of everything that makes up our world, including ourselves. In this free course, Water for life, you will learn the basic chemistry of how these components work together, starting with a chemical compound we are all very familiar with water. First published on Wed, 17 Jan 2018 as Author(s): Creator not set

Climate change
Climate change is a key issue on today's social and political agenda. This free course explores the basic science that underpins climate change and global warming. First published on Tue, 30 Oct 2018 as Climate change. To find out more visit The Open University's Author(s): Creator not set

Effects of pollutants on the aquatic environment
Effects of pollutants on the aquatic environment is a free course. It begins with an introduction to water and goes on to briefly outline the major sources of water pollution (these being sewage works, manufacturing and industrial plants, the farming and animal husbandry sectors, landfill sites and urban surface water run-off). It considers the major water pollutants and describes the effects they have on water. Author(s): Creator not set