3.4 Cylinders and shapes with a uniform cross-section An important idea when calculating volumes of simple shapes is that of a cross-section. In the case of the rectangular box considered above, it is possible to slice through the box horizontally so that the sliced area is exactly the same as the area of the base or top; in other words, the areas of the horizontal cross-sections are equal. 3.3 Volumes 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 – but not vice versa. Note that a container with a particular volume will not nec Try some yourself Find the area of a circle of (a) radius 8 cm, and (b) radius 15 m. (a) Try some yourself Find the area of each of these shapes. Try some yourself Calculate all the angles at the centres of these objects. 4.2 A better solution Here is an improved solution which shows working. 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. 4.4 ‘Show that ’ questions In this type of question you are given the answer! All the marks are allocated for correct reasoning and justification. 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): 1.2 Representation and language 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 7 Solutions to the exercises Section 6 contains solutions to the exercises that appear throughout sections 1-5. Click the link below to open the solutions (13 pages, 232KB). 3.2 Converting to a percentage Fractions and decimals can also be converted to percentages, by multiplying by 100%. So, for example, 0.17, 0.3 and   0.17 × 100% = 17%; 1.1 Introduction Ratios crop up often in official statistics. The government wants the teacher–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 Acknowledgements 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 1.2.3 Process 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 World in transition: Managing Resources Understanding the environment: Learning and communication Introducing the environment: Ecology and ecosystems Climate change Effects of pollutants on the aquatic environment Understanding water quality Surviving the winter
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can be expressed as percentages as follows:
Do you take your access to water for granted? The Peruvian and Tanzanian communities featured in this album certainly don’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
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.
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):
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):
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.
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Water is arguably the most important physical resource as it is the one that is essential to human survival. Understanding the global water cycle and how we use water is essential to planning a sustainable source of water for the future. In the UK there are areas where water supplies are limited, shown by recent droughts. Globally, there are many areas that do not have enough water to support the current population adequately. Decisions will have to be made on the best way to use water in a worl
In this free course, Surviving the winter, we study one aspect of the fluctuating nature of an organisms environment. We consider how organisms living in a temperate climate, such as that in Britain, are adapted to cope with winter. You will see that there is much diversity of adaptations among organisms, with different species coping with the demands of a fluctuating environment in quite different ways. As cyclic variations are a widespread feature of environments, the range of adaptations to t