A prism is a three dimensional shape that has the same cross section throughout its length.
As a technicality, the long axis of the shape should be straight and not bent in any way.
If you think of a lump of clay moulded into a cylinder, you have a prism, but if you bend the cylinder so the main axis is no longer absolutely straight, it cannot be termed a 'prism'.
A coiled cable is not a prism, but if it were to be opened out and stretched very tight, it might well become one.
If the end faces are at right angles to the long axis, the prism is termed a 'right' prism.
If not, the prism is termed an 'oblique' prism.
In the mathematics classroom we are introduced to cylinders, tubes, cuboids, hexagonal prisms, octagonal prisms and so on, but in the world around us we find many other types of prisms.
Almost all extruded components are prisms (often very long ones) and these can take many cross-sectional shapes - L, T.
E sections, for instance.
Rolled girders can be T or I shape, and plastic and earthenware products can have almost any cross section you care to mention.
Some prisms are very thin such as triangular road signs with rounded corners which may only be a few millimetres thick.
When explaining this to children, get them to imagine that each sign has been cut from a long piece of metal whose cross section is the same as the front face.
Some are larger such as rubbish skips (dumpsters).
The trick here is to think of the side as being the 'end', i.
e.
the cross section that remains constant throughout the length of the shape.
Swimming pools can also be prisms.
Think of a normal public swimming pool.
If you were to walk from the shallow end towards the deep end (holding your breath, naturally), you would first encounter a section that is almost level, then quite a steep slope towards the middle of the pool and finally a flat section at the deep end.
Now imagine that you are standing on the side of the pool looking across to the other side.
The 'side' you are standing on is now the 'end' from the prism's point of view as this is the cross section that is the same throughout its length.
(the width of the pool).
Once you take this view, you notice that many more shapes are prisms than you may have thought possible, such as greenhouses, octagonal pizza boxes, skirting boards and rolls of tape.
In practice, of course, real objects such as greenhouses have small additional pieces (window frames, door handles), but children are quite happy ignoring these and focussing on the overall shape.
Why are prisms so important in mathematics? The reason is that often we need to find the volume of an object and if that object can be identified as a prism, finding its volume is a relatively simple matter.
Suppose, for example, you ran a smallholding producing fruit in a large greenhouse, you would need to know its volume in order to be able to calculatethe number and power of the heaters needed to maintain the correct temperature.
If you were thinking of installing a swimming pool, you would want to know how much water it will hold as you will probably be paying for this by the cubic metre.
The last question to consider, therefore, is: 'How do you calculate the volume of a prism?' The answer is surprisingly simple: Find the area of the end (that is, the cross sectional area) and multiply by the length of the prism.
If you are dealing with a hollow prism such as a length of copper pipe, you can find the cross sectional area by first finding the area of the outer circle, then finding the area of the inner circle and finally subtracting the two answers.
Multiplying this figure by the length will give the volume of copper used.
It is possible now to see why, when calculating the volume of shapes such as rubbish skips and swimming pools, we think of the 'side' as being the 'end' as that is the shape of the cross section.
These questions come up very often in GCSE examination papers and if they arise in the non-calculator paper, it is necessary to have a good knowledge of times tables.
As a technicality, the long axis of the shape should be straight and not bent in any way.
If you think of a lump of clay moulded into a cylinder, you have a prism, but if you bend the cylinder so the main axis is no longer absolutely straight, it cannot be termed a 'prism'.
A coiled cable is not a prism, but if it were to be opened out and stretched very tight, it might well become one.
If the end faces are at right angles to the long axis, the prism is termed a 'right' prism.
If not, the prism is termed an 'oblique' prism.
In the mathematics classroom we are introduced to cylinders, tubes, cuboids, hexagonal prisms, octagonal prisms and so on, but in the world around us we find many other types of prisms.
Almost all extruded components are prisms (often very long ones) and these can take many cross-sectional shapes - L, T.
E sections, for instance.
Rolled girders can be T or I shape, and plastic and earthenware products can have almost any cross section you care to mention.
Some prisms are very thin such as triangular road signs with rounded corners which may only be a few millimetres thick.
When explaining this to children, get them to imagine that each sign has been cut from a long piece of metal whose cross section is the same as the front face.
Some are larger such as rubbish skips (dumpsters).
The trick here is to think of the side as being the 'end', i.
e.
the cross section that remains constant throughout the length of the shape.
Swimming pools can also be prisms.
Think of a normal public swimming pool.
If you were to walk from the shallow end towards the deep end (holding your breath, naturally), you would first encounter a section that is almost level, then quite a steep slope towards the middle of the pool and finally a flat section at the deep end.
Now imagine that you are standing on the side of the pool looking across to the other side.
The 'side' you are standing on is now the 'end' from the prism's point of view as this is the cross section that is the same throughout its length.
(the width of the pool).
Once you take this view, you notice that many more shapes are prisms than you may have thought possible, such as greenhouses, octagonal pizza boxes, skirting boards and rolls of tape.
In practice, of course, real objects such as greenhouses have small additional pieces (window frames, door handles), but children are quite happy ignoring these and focussing on the overall shape.
Why are prisms so important in mathematics? The reason is that often we need to find the volume of an object and if that object can be identified as a prism, finding its volume is a relatively simple matter.
Suppose, for example, you ran a smallholding producing fruit in a large greenhouse, you would need to know its volume in order to be able to calculatethe number and power of the heaters needed to maintain the correct temperature.
If you were thinking of installing a swimming pool, you would want to know how much water it will hold as you will probably be paying for this by the cubic metre.
The last question to consider, therefore, is: 'How do you calculate the volume of a prism?' The answer is surprisingly simple: Find the area of the end (that is, the cross sectional area) and multiply by the length of the prism.
If you are dealing with a hollow prism such as a length of copper pipe, you can find the cross sectional area by first finding the area of the outer circle, then finding the area of the inner circle and finally subtracting the two answers.
Multiplying this figure by the length will give the volume of copper used.
It is possible now to see why, when calculating the volume of shapes such as rubbish skips and swimming pools, we think of the 'side' as being the 'end' as that is the shape of the cross section.
These questions come up very often in GCSE examination papers and if they arise in the non-calculator paper, it is necessary to have a good knowledge of times tables.
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