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## Pyramids and Cones in Mathematics Lessons

Math teachers usually have wooden or plastic shaped boxes tucked deep in their cupboards that they bring out when they teach the principles of cones and pyramids, but often they are complete – right up to the edge. Of course, cones or pyramids have a lot of math, but their use in everyday life is limited. You will find ice cream cones and hanging baskets in the shape of cones, but the wholes must be either hand held, supported by wire or wires or standing on their bases, all of which restrict their use (unless you want to buy thousands of street work cones).

It is the same with the pyramid. Again we’re limited to hanging baskets and the like and unless you want to bury the pharaoh, they’re not much use standing on their base.

Enter __cut off__ Cones and pyramids. In simple terms, a truncated cone or pyramid is a complete one with the top removed. If the cut is made parallel to the base, the shape is called ‘truncated’. (If the cut is not parallel to the base it is called a ‘diagonal cut’, but these shapes are less often used in the construction of physical objects than perfect shapes.)

But now we are in a completely different ball game as truncated cones and pyramids are admirably suited for stacking and we see them everywhere. Have your kids look for them at garden centers, crockery shops, DIY shops and so on. A beautiful example is the type of drinking mug that is sold with a small Easter egg. They are usually shaped like a well-cut cone with a simple handle added.

I recently saw a metal dustbin (the sort used for burning papers, garden waste etc) at my local garden centre. The main component was an inverted truncated cone with legs. The lid was a short but wide truncated cone with two handles, one on each side to make room for a chimney… you guessed it!

Non-pointed cones are also used for lamp shades, flower pots, fruits, dovecots, rocket engine nozzles and phase caps.

Truncated pyramids are found in concrete lampposts (at first glance you might think these are prisms, but they usually decrease in cross-sectional area as the height increases), concrete blocks in roadworks, office waste bins, lampshades, wheelbars and many other things such as a bird bath and fountain. Objects A mass of objects joined together.

Finding the volume of a cone or pyramid is a great mathematical exercise and requires a good knowledge of a calculator or times table. If we imagine a prism surrounding a cone or pyramid and the same height, the volume is always one-third the volume of the prism, which gives us the formula V = base area x height ÷3.

It is possible to find the volume of a truncated cone or pyramid using a more complex formula, but at GCSE level it is better to find the volume of the full size and then subtract the volume of the piece removed.

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