Mathematics teachers usually have a box of wooden or plastic shapes that lie deep in the cabinet of good things that they teach when teaching the theorems and pyramids, but they are mostly complete – all the way to the sharp end. Of course, there are many maths in the cone or pyramids, but in their everyday life their use is limited. You have ice-horses and cone-shaped hangers available, but complete should be kept in hand, supported by wire or wire or standing on their bases, all limiting their use (unless you do not want to buy thousands of cone designs).
It’s the same with the pyramids. We are again limited to hanging baskets and the like, and if you do not want to bury pharaohs, they do not have much benefit standing on their bases.
Enter the truncated cone and pyramid. Simply put, the truncated cone or pyramid is full of the upper part. If the cut is made parallel to the base, the shape is simply called “shortened”. (If the cut is not parallel to the base, it is called a ‘truncated trunk’, but these shapes have even less utility in building physical objects than full shapes.)
But now we are in a totally different ball game like shortened cones and pyramids are an excellent set of stacking and we can see them everywhere. Have your children watch out for them in garden centers, pottery stores, DIY stores and so on. A wonderful example is the type of beverage drink that is sold with a small Easter egg. Usually they are well shaped in the shape of a bony cone with a simple hand.
I recently saw metal dust (a kind used for burning paper, garden waste, etc.) in my garden. The main component was a crossed truncated cones with legs. The lid was a short, but wide, shortened cone with two handles, one on each side, to allow the chimney area to … hit!
Pointless cones are also used for lamps, flower pots, fruit pans, pigeons, motorcycle jets and fez caps, but only a few.
Shortened pyramids are found in concrete lamps (first glance can suggest that you think that they are prisms, but they normally decrease in the transverse area as the height increases), concrete blocks on the road, office garbage, lamps, trolleys and a multitude of items that consist of several connected, such as bird baths and fountains.
Finding the volume of a cone or pyramid is a great math exercise and requires a calculator or a good knowledge of time tables. If we imagine the prism around the cone or pyramid and the same height, the volume is always a third of the prism volume, giving us the formula V = the base area x the height ÷ 3.
It is possible to find the volume of the truncated cone or pyramid using more complex formulas, but at the GCSE level, it is best to find the volume of the full form, and then subtract the volume of the removed part.