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Submitted questions and ideas from AQA teachers

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Submitted questions and ideas from AQA teachers

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Dave Gale's plan for Paper 2 pre-release

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Dave Gale's plan for Paper 2 pre-release

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Simply:

1. Display this photograph (or similar)

2. Ask "Where is the Maths in that?"

3. Let the ideas flow!

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Useful 2 min career video to help students ease in to the context

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Useful 2 min career video to help students ease in to the context

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Explore careers: renewable technology engineer

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Taskmaster - how many balls in the basket?

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Taskmaster - how many balls in the basket?

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Taskmaster l How many balls are in the basket?

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Could start by showing just the graph and asking 'What's Going on in this Graph?' - how to run this activity explained here

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Could start by showing just the graph and asking 'What's Going on in this Graph?' - how to run this activity explained here

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Introduction to ‘What’s Going On in This Graph?’ (Published 2021)

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Want to learn more about this feature? Watch this short introduction video and start using New York Times graphs in your classroom.

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Tips on how to get students curious about graphs/information

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Tips on how to get students curious about graphs/information

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Slow Reveal Graph is an instructional routine that promotes sensemaking about data. This highly engaging routine uses scaffolded visuals and discourse to help students (in K-12 and beyond) make sense of data. As more and more of the graph is revealed, students refine their interpretation and construct meaning, often in surprising ways.

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The Best Way to Pack Spheres - Numberphile

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The Best Way to Pack Spheres - Numberphile

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The Best Way to Pack Spheres - Numberphile

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Other useful graphs from Our World in Data

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Other useful graphs from Our World in Data

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Electricity is one of three components that make up total energy production. The other two are transport and heating.

As we look at in more detail in this article, the breakdown of sources - coal, oil, gas, nuclear and renewables - is therefore different in the electricity versus the energy mix. Generally, low-carbon sources (nuclear and renewables) account for a larger share in our electricity mix than our total energy mix.

This means it's important to distinguish between the two. In another page we provide the full breakdown of the Energy Mix. But in this article we focus on the Electricity Mix.

Where do we get our electricity from? Which countries have the cleanest electricity grids? In this article we look at the breakdown across the world.

Electricity is only one part of total energy - decarbonizing electricity is only one step towards a low-carbon energy system

Solar and wind generation are growing quickly across the world. This is, of course, good news as we try to shift our energy systems away from fossil fuels.

Such progress often makes the headlines. Here is one example from this year:

→ More UK energy is coming from clean sources than fossil fuels for the first time ever, National Grid announces (Independent, 2020)

At first glance, we might think that we are edging close to a fossil-free energy system.

Unfortunately, many of these headlines are misleading.¹ The Independent made the mistake of using the terms electricity and energy interchangeably, when they are actually not the same thing.

Electricity (or 'power') is just one component of total energy consumption. The other two components being transport and heating.

When we see headlines about our progress on decarbonization, the quoted figures often refer to electricity. Many countries are making progress on clean electricity, but progress on energy as a whole is much slower.

Let's compare the breakdown of the global energy and electricity mix - these are shown in the chart.

We see a large difference between the share that comes from low-carbon sources. Nuclear and renewables account for more than one-third (36.7%) of global electricity. But they account for less than half that figure (15.7%) of the global energy mix. This is because the other elements of the energy demand - transport and heating - rely much more heavily on fossil fuels.

But there is another aspect to consider. The fact that transport and heating are harder to decarbonize, clean electricity will become ever-more important. Many solutions rely on us electrifying other parts of the energy system - such as shifting to electric vehicles. The International Energy Agency, for example, projects that by 2030, global electricity demand for electric vehicles will increase five- to eleven-fold from levels in 2019. If we are to reap the climate benefits of electric vehicles, this electricity needs to be as low-carbon as possible.

But when we see headlines on progress in decarbonizing the electricity sector we need to remember that it is just one part of the energy story. If we don't, we risk falling into a false sense of progress and let leaders, governments and companies boast targets that are not nearly ambitious enough.

Where does our electricity come from?

What sources make up our electricity mix? How much comes from coal, oil, gas, and how much from nuclear, hydropower, solar or wind?

In the interactive charts shown here we see the breakdown of the electricity mix by source.

The stacked area chart shows electricity production in absolute terms. It allows you see how these sources sum up. The line chart shows each source's share of the total, and gives a better perspective on how each is changing over time.

Globally we see that coal, followed by gas, is the largest source of electricity production. Of the low-carbon sources, hydropower and nuclear make the largest contribution; although wind and solar are growing quickly.

If we look at the electricity mix of particular countries [you can do this using the "Change country" button on the bottom-left of the chart] we can see dramatic changes in over time. Take the UK as an example: there we see a dramatic decline in the role of coal in its electricity mix. In the late 1980s, coal account for more than 60% of electricity production. By 2019 this had fallen to 2%.

How you can interact with these charts

In the charts here we see the breakdown of the electricity mix by country. First with the higher-level breakdown by fossil fuels, nuclear and renewables. Then with the specific breakdown by source, including coal, gas, oil, nuclear, hydro, solar, wind and other renewables (which include bioenergy, wave and tidal).

This is given in terms of per capita consumption. Using the toggle on the interactive charts you can also see the percentage breakdown for each source using the 'Relative' tickbox.

How much of our electricity comes from low-carbon sources?

Around 16% of global energy (15.7% to be precise) comes from low-carbon sources - that is, the sum of nuclear energy and renewables.

But energy and electricity are not the same - despite the fact that many people use these terms interchangeably. Electricity (sometimes referred to as 'power') is only a subset of total energy production, which also includes heating and transport.

How much of our electricity comes from low-carbon sources?

37% of global electricity production comes from low-carbon sources

In the chart we see the percentage of global electricity production that comes from nuclear or renewable energy, such as solar, wind, hydropower, wind and tidal and some biomass.

Globally, 36.7% of our electricity was low-carbon in 2019. More than one-third. The remaining two-thirds come from fossil fuels - mostly coal and gas.

This is more than double the share in the total energy mix, where nuclear and renewables only account for 15.7%. We looked at the comparison of the global energy and electricity mix here. When people quote a high number for the share of low-carbon energy in the electricity mix we need to be aware of the fact that electricity is only part of the energy equation. The share in the total energy mix is much smaller.

Disappointingly, the percentage of electricity that comes from low-carbon sources today is almost unchanged from the mid-1980s. In fact, throughout the early-2000s this share actually regressed. In the following section we will see that progress was slow because nuclear output declined at a time when renewables have been growing.

Low-carbon electricity: around 26% of global electricity comes from renewables, and 10% from nuclear

What is the breakdown of our electricity supply in terms of fossil fuels, renewable energy and nuclear power?

In 2019, almost two-thirds (63.3%) of global electricity came from fossil fuels. Of the 36.7% from low-carbon sources, renewables accounted for 26.3% and nuclear energy for 10.4%.

As we noted earlier, the relative contribution of fossil fuels and low-carbon electricity has been pretty stagnant for decades. In fact, in the early 2000s, fossil fuels even gained ground. Over this period, nuclear's share declined whilst renewables grew. We see this in the chart. The progress made in renewables has been offset by a decline in nuclear energy; nuclear declined by almost as much as renewables gained.

Some countries get most of their electricity from low-carbon sources

Globally we get just over one-third of our electricity from low-carbon sources. But some countries get much more - some nearly all of it - from fossil-free sources.

In the interactive map shown we see this share across the world. Some countries get over 90% of their electricity from nuclear or renewables - Sweden, Norway, France, Paraguay, Iceland, and Nepal, among others.

You can explore the electricity mix - broken down by individual source - for countries in our work here. Nearly all of these countries have one thing in common: they get a lot of electricity from hydropower and/or nuclear energy. Solar, wind and other renewable technologies are growing quickly and will hopefully account for a large share of electricity production in the future - but the countries who have a low-carbon electricity mix today have relied heavily on hydroelectric and nuclear power in recent years.

We must take these country-level examples and learn from them. In the years to come, accelerating the transition to clean electricity will become ever-more important as we electrify other parts of the energy system too (shifting to electric vehicles, for example). We will need to rely on low-carbon electricity, and lots of it.

Carbon intensity of electricity

Carbon intensity of electricity measures the amount of CO2 that is produced per unit of electricity. It is measured as the grams of CO2 produced per kilowatt-hour (kWh).

Countries which get a large share of their electricity from low-carbon sources (renewables and nuclear) will have a lower carbon intensity.

This interactive map shows the carbon intensity of electricity across Europe. Ember - our key electricity data source - currently only provides carbon intensity data for the EU-27 countries, plus the United Kingdom.

Electricity production by source

Coal is currently the largest source of electricity globally. For many countries remains the dominant source. But, we also see that others have seen a massive shift away from coal in recent years - the UK is one such example.

This interactive map shows the share of electricity that comes from coal across the world.

Gas is now the second largest source of electricity production globally.

Its contribution is growing quickly in many countries as they substitute it for coal in the electricity mix. From a climate perspective, this transition is positive since gas typically emits less CO₂ per unit of energy. But, we still ultimately want to shift away from gas towards low-carbon sources such as renewables and nuclear.

This interactive map shows the share of electricity that comes from gas across the world.

Hydropower makes a large contribution to low-carbon electricity across the world. Globally it accounts for around 17% of production.

This interactive map shows the share of electricity that comes from hydropower across the world.

This interactive map shows the share of electricity that comes from solar power across the world.

Three tips on how to interact with this map

Wind accounts for just 5% to 6% of global electricity production. But wind generation has been growing rapidly in many countries across the world in recent years.

This interactive map shows the share of electricity that comes from wind across the world.

Explore more of our work on Energy

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Electricity is one of three components that make up total energy production. The other two are transport and heating. As we look at in more detail in this article, the breakdown of sources - coal, oil, gas, nuclear and renewables - is therefore different in the electricity versus the energy mix.

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Energy featured in Edexcel pre-release 2017

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Energy featured in Edexcel pre-release 2017

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Welcome to YM Packaging UK channel! Are you looking for packaging machinery? From YM Packaging Group UK, it will be a pleasure to assist you. YM PACKAGING GROUP offers complete lines solutions, combining our experience and the professionalism of our human team, we can effectively automate the pa…

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Dear Dr Maths, At a recent fundraising event I attended there was an activity to guess the number of sweets in the jar. Is there a mathematical way to improve your chance of being correct?

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Intro to Income Tax for Core Maths 2021 2022

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National Insurance tutorial for the 2022 Core Maths exam

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In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three- dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.

A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the packing density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume.

For equal spheres in three dimensions, the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 64%.

A arrangement (commonly called a regular arrangement) is one in which the centers of the spheres form a very symmetric pattern which needs only n vectors to be uniquely defined (in n- dimensional Euclidean space). Lattice arrangements are periodic. Arrangements in which the spheres do not form a lattice (often referred to as irregular) can still be periodic, but also (properly speaking non-periodic) or . Because of their high degree of symmetry, lattice packings are easier to classify than non-lattice ones. Periodic lattices always have well-defined densities.

Dense packing

In three-dimensional Euclidean space, the densest packing of equal spheres is achieved by a family of structures called close-packed structures. One method for generating such a structure is as follows. Consider a plane with a compact arrangement of spheres on it. Call it A. For any three neighbouring spheres, a fourth sphere can be placed on top in the hollow between the three bottom spheres. If we do this for half of the holes in a second plane above the first, we create a new compact layer. There are two possible choices for doing this, call them B and C. Suppose that we chose B. Then one half of the hollows of B lies above the centers of the balls in A and one half lies above the hollows of A which were not used for B. Thus the balls of a third layer can be placed either directly above the balls of the first one, yielding a layer of type A, or above the holes of the first layer which were not occupied by the second layer, yielding a layer of type C. Combining layers of types A, B, and C produces various close-packed structures.

Two simple arrangements within the close-packed family correspond to regular lattices. One is called cubic close packing (or face-centred cubic, "FCC")-where the layers are alternated in the ABCABC... sequence. The other is called hexagonal close packing ("HCP")-where the layers are alternated in the ABAB... sequence. But many layer stacking sequences are possible (ABAC, ABCBA, ABCBAC, etc.), and still generate a close-packed structure. In all of these arrangements each sphere touches 12 neighboring spheres, and the average density is

Carl Friedrich Gauss proved in 1831 that these packings have the highest density amongst all possible lattice packings.

In 1611 Johannes Kepler conjectured that this is the maximum possible density amongst both regular and irregular arrangements-this became known as the Kepler conjecture. In 1998, Thomas Callister Hales, following the approach suggested by László Fejes Tóth in 1953, announced a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving checking of many individual cases using complex computer calculations. Referees said that they were "99% certain" of the correctness of Hales' proof. On 10 August 2014, Hales announced the completion of a formal proof using automated proof checking, removing any doubt.

Other common lattice packings

Some other lattice packings are often found in physical systems. These include the cubic lattice with a density of , the hexagonal lattice with a density of and the tetrahedral lattice with a density of , and loosest possible at a density of 0.0555.[4]

Jammed packings with a low density

Packings where all spheres are constrained by their neighbours to stay in one location are called rigid or jammed. The strictly jammed sphere packing with the lowest density is a diluted ("tunneled") fcc crystal with a density of only 0.49365.

If we attempt to build a densely packed collection of spheres, we will be tempted to always place the next sphere in a hollow between three packed spheres. If five spheres are assembled in this way, they will be consistent with one of the regularly packed arrangements described above. However, the sixth sphere placed in this way will render the structure inconsistent with any regular arrangement. This results in the possibility of a random close packing of spheres which is stable against compression. Vibration of a random loose packing can result in the arrangement of spherical particles into regular packings, a process known as granular crystallisation. Such processes depend on the geometry of the container holding the spherical grains.

When spheres are randomly added to a container and then compressed, they will generally form what is known as an "irregular" or "jammed" packing configuration when they can be compressed no more. This irregular packing will generally have a density of about 64%. Recent research predicts analytically that it cannot exceed a density limit of 63.4% This situation is unlike the case of one or two dimensions, where compressing a collection of 1-dimensional or 2-dimensional spheres (that is, line segments or circles) will yield a regular packing.

The sphere packing problem is the three-dimensional version of a class of ball-packing problems in arbitrary dimensions. In two dimensions, the equivalent problem is packing circles on a plane. In one dimension it is packing line segments into a linear universe.

In dimensions higher than three, the densest regular packings of hyperspheres are known up to 8 dimensions. Very little is known about irregular hypersphere packings; it is possible that in some dimensions the densest packing may be irregular. Some support for this conjecture comes from the fact that in certain dimensions (e.g. 10) the densest known irregular packing is denser than the densest known regular packing.

In 2016, Maryna Viazovska announced a proof that the provides the optimal packing (regardless of regularity) in eight-dimensional space, and soon afterwards she and a group of collaborators announced a similar proof that the Leech lattice is optimal in 24 dimensions. This result built on and improved previous methods which showed that these two lattices are very close to optimal. The new proofs involve using the Laplace transform of a carefully chosen modular function to construct a radially symmetric function f such that f and its Fourier transform f̂ both equal one at the origin, and both vanish at all other points of the optimal lattice, with f negative outside the central sphere of the packing and f̂ positive. Then, the Poisson summation formula for f is used to compare the density of the optimal lattice with that of any other packing. Before the proof had been formally refereed and published, mathematician Peter Sarnak called the proof "stunningly simple" and wrote that "You just start reading the paper and you know this is correct."

Another line of research in high dimensions is trying to find asymptotic bounds for the density of the densest packings. As of 2017, it is known that for large n, the densest lattice in dimension n has density between (for some constant c) and . Conjectural bounds lie in between.

Unequal sphere packing

Many problems in the chemical and physical sciences can be related to packing problems where more than one size of sphere is available. Here there is a choice between separating the spheres into regions of close-packed equal spheres, or combining the multiple sizes of spheres into a compound or interstitial packing. When many sizes of spheres (or a distribution) are available, the problem quickly becomes intractable, but some studies of binary hard spheres (two sizes) are available.

When the second sphere is much smaller than the first, it is possible to arrange the large spheres in a close-packed arrangement, and then arrange the small spheres within the octahedral and tetrahedral gaps. The density of this interstitial packing depends sensitively on the radius ratio, but in the limit of extreme size ratios, the smaller spheres can fill the gaps with the same density as the larger spheres filled space. Even if the large spheres are not in a close-packed arrangement, it is always possible to insert some smaller spheres of up to 0.29099 of the radius of the larger sphere.

When the smaller sphere has a radius greater than 0.41421 of the radius of the larger sphere, it is no longer possible to fit into even the octahedral holes of the close-packed structure. Thus, beyond this point, either the host structure must expand to accommodate the interstitials (which compromises the overall density), or rearrange into a more complex crystalline compound structure. Structures are known which exceed the close packing density for radius ratios up to 0.659786.

Upper bounds for the density that can be obtained in such binary packings have also been obtained.

In many chemical situations such as ionic crystals, the stoichiometry is constrained by the charges of the constituent ions. This additional constraint on the packing, together with the need to minimize the Coulomb energy of interacting charges leads to a diversity of optimal packing arrangements.

Although the concept of circles and spheres can be extended to hyperbolic space, finding the densest packing becomes much more difficult. In a hyperbolic space there is no limit to the number of spheres that can surround another sphere (for example, Ford circles can be thought of as an arrangement of identical hyperbolic circles in which each circle is surrounded by an infinite number of other circles). The concept of average density also becomes much more difficult to define accurately. The densest packings in any hyperbolic space are almost always irregular.

Despite this difficulty, K. Böröczky gives a universal upper bound for the density of sphere packings of hyperbolic n-space where n ≥ 2. In three dimensions the Böröczky bound is approximately 85.327613%, and is realized by the horosphere packing of the order-6 tetrahedral honeycomb with Schläfli symbol {3,3,6}. In addition to this configuration at least three other horosphere packings are known to exist in hyperbolic 3-space that realize the density upper bound.

Touching pairs, triplets, and quadruples

The contact graph of an arbitrary finite packing of unit balls is the graph whose vertices correspond to the packing elements and whose two vertices are connected by an edge if the corresponding two packing elements touch each other. The cardinality of the edge set of the contact graph gives the number of touching pairs, the number of 3-cycles in the contact graph gives the number of touching triplets, and the number of tetrahedrons in the contact graph gives the number of touching quadruples (in general for a contact graph associated with a sphere packing in n dimensions that the cardinality of the set of n-simplices in the contact graph gives the number of touching ( n + 1)-tuples in the sphere packing). In the case of 3-dimensional Euclidean space, non-trivial upper bounds on the number of touching pairs, triplets, and quadruples were proved by Karoly Bezdek and Samuel Reid at the University of Calgary.

The problem of finding the arrangement of n identical spheres that maximizes the number of contact points between the spheres is known as the "sticky-sphere problem". The maximum is known for n ≤ 11, and only conjectural values are known for larger n.

Sphere packing on the corners of a hypercube (with the spheres defined by Hamming distance) corresponds to designing error-correcting codes: if the spheres have radius t, then their centers are codewords of a (2 t + 1)-error-correcting code. Lattice packings correspond to linear codes. There are other, subtler relationships between Euclidean sphere packing and error-correcting codes. For example, the binary Golay code is closely related to the 24-dimensional Leech lattice.

For further details on these connections, see the book Sphere Packings, Lattices and Groups by Conway and Sloane.

A non-technical overview of packing in hyperbolic space.

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In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three- dimensional Euclidean space.

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Mapped: How the UK generates its electricity

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Mapped: How the UK generates its electricity

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Energy Mapped: How the UK generates its electricity

| October 12. 2015. 11:05

In recent years, the UK has added thousands of renewable power schemes to its ageing — and dwindling — fleet of coal, nuclear and gas plants. Yet these older sources still supply most of the UK's electricity.

Carbon Brief has plotted the nation's power stations in an interactive map to show the diversity of the UK's electricity supply.

The maps also show how the UK's hydroelectric generation is limited to Scotland and Wales, where plentiful rainfall, mountains and sparsely populated valleys make it easier to build dams. The largest circles are the UK's pumped storage reservoirs, which act like giant batteries for the grid.

Windfarms are skewed, too, towards the coastlines and higher ground where consistent wind speeds are more reliable. You can also see larger offshore wind installations popping up - for now these are relatively close to the shore, in shallower waters.

The UK's coal, gas and nuclear sites are more evenly distributed, but here, too, the map is revealing. All nuclear sites, for instance, are on the coast, because they need guaranteed access to plentiful supplies of cooling water.

Historic shifts

A closer look at the data behind the map reveals some interesting shifts in the types of infrastructure being built to generate the UK's electricity. In the late 1960s and early 1970s, many large coal plants were built that are still operating today (black bars, below).

Our nuclear sites were built over the course of a quarter century from 1971 (purple bars). From the 1990s, new gas-fired plant was added during the UK's "dash for gas" (blue). And since the turn of the century there has been a massive expansion of renewable capacity (green).

Like the map, this shifting history tells us more than you might expect. For instance, the big gaps between nuclear additions show how long it takes to build atomic plant. You can also see why our current coal fleet has an average age of 44 years with Drax, the newest coal plant in Great Britain, completed in 1986. Yet the UK still has nearly 20 gigawatts (GW) of coal capacity.

However, the UK has no clear to change its still-heavy reliance on coal. Despite a relatively high carbon price and prime minister David Cameron's to phase the fuel out, some 31% of UK electricity last year came from coal (black area, below).

That said, UK coal use fell by a last year, as overall electricity use to mid-1990s levels. Three UK coal plants totalling 5GW have recently announced plans to close in March 2016. These are the 2GW Eggborough , 1GW Ferrybridge C and 2GW plants.

There has been a steady stream of over recent years as old and dirty coal plants have shut down, rather than invest in air pollution controls (shrinking black areas in the chart, below). Coal's days may be numbered if a rumoured phase-out date of 2023 is confirmed.

Renewable capacity

Meanwhile, some 16GW of new renewables have been built over the past five years, accounting for four-fifths of new capacity in that period. Gas made up the remainder, though only renewables have been added since the start of 2013.

De-rated capacity is falling. Combined with the unprofitability of building new gas-fired generation, this is creating a UK " capacity crunch ". In response to this shrinking margin between supply and demand, the UK's capacity market will begin to pay power stations, just for being available - or it will pay large users to reduce their peak demand .

A chorus of concern over capacity from some analysts and sections of the media is consistently rebuffed by National Grid and the government, which insist plans are in place to keep the lights on. Sub-sea electricity interconnectors, shown in our map and with capacity set to more than double over the next five years, will also help to buffer ups and downs in the UK's supply and demand.

Main Map: The UK's electricity generating sites and sub-sea interconnectors. Only currently operating sites of 1 megawatt (MW) capacity or larger are included. The size of the circles is proportional to site capacity but a minimum size applies below a certain threshold. Toggle the buttons to view each fuel type alone. Hover over each site to see further information on its capacity and age. Data comes from the Department for Energy and Climate Change (DECC) and Carbon Brief research. Credit: Rosamund Pearce, Carbon Brief. You can also visit the full-screen version.

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Mapped: How the UK generates its electricity | Carbon Brief

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Our interactive map shows how and where the UK's electricity is generated.

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Energy Dashboard - real time and historical electricity generation data

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Energy Dashboard - real time and historical electricity generation data

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Energy Dashboard - real time and historical GB electricity data, carbon emissions and UK generation sites mapping

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Live and historical GB National Grid electricity data, showing generation, demand and carbon emissions and UK generating sites mapping.

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Sweet science: Common candies yield physics discovery

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News from PRINCETON UNIVERSITY Office of Communications 22 Chambers St. Princeton, New Jersey 08542 Telephone 609-258-3601; Fax 609-258-1301 For immediate release: February 12, 2004 Media contact: Steven Schultz, (609) 258-5729, sschultz@princeton.edu Editors: Photos are available at: http://www.princeton.edu/pr/news/04/q1/img/Chaikin-Torquato/ Sweet science: Common candies yield physics discovery Research using M&M's sheds light on particle-packing problem PRINCETON, N.J.

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Calculating the optimal sphere packing density: with oranges

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Diamond smuggling activity Requires estimation and the formula for the volume of a cylinder

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Diamond smuggling activity Requires estimation and the formula for the volume of a cylinder

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Please be aware that resources have been published on the website in the form that they were originally supplied. This means that procedures reflect general practice and standards applicable at the time resources were produced and cannot be assumed to be acceptable today. Website users are fully responsible for ensuring that any activity, including practical work, which they carry out is in accordance with current regulations related to health and safety and that an appropriate risk assessment has been carried out.

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This Core Maths activity investigates diamond smuggling. The presentation gives details of how diamonds were smuggled out of Namibia in cans of pilchards. Students need to use the information given to calculate an estimate of the value of the smuggled diamonds. They need to use estimation and the formula for the volume of a cylinder.