Teachers of mathematics usually have a box of wooden or plastic figures tucked deep in their dresser delicacies, which they manifest when learning the theories of cones and pyramids, but mostly they are full - up to a sharp end. Of course, there is a lot of mathematics in a cone or a pyramid, but in everyday life their use is limited. You will find ice cream cones and hanging cones in the shape of a cone, but the full ones must either be held in hand, supported by threads or wires, or stand on their bases, all this limits their use (except for the desire to buy thousands of road cones).
The same with the pyramids. Again, we are limited to hanging baskets, etc., and without you wanting to bury Pharaoh, they do not have much space on their grounds.
Enter truncated cone and pyramid. Simply put, a truncated cone or pyramid is complete with the top removed. If the incision is made parallel to the base, the shape is simply called truncated. (If the cut is not parallel to the base, it is called “oblique truncated”, but these forms are even less used in the construction of physical objects than full shapes).
But now we are in a completely different ball game, since the truncated cones and pyramids are excellent for styling, and we see them everywhere. Ask your children to keep an eye on them at garden centers, tableware stores, DIY stores, etc. A great example is the type of beer mugs that are sold with a small Easter egg. They are usually well processed in the shape of a truncated cone with a simple handle added.
I recently saw metal trash (sorting used for burning paper, garden waste, etc.) at my local garden center. 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, so that the space for the chimney was ... you guessed it!
Eyeglass cones are also used for lamp shades, flower pots, fruit bowls, pigeons, rocket nozzles and fez caps, and these are just some of them.
Truncated pyramids are found in concrete lampposts (at first glance it may lead to the idea that these are prisms, but they usually reduce the cross-sectional area as the height increases), concrete blocks for road works, office trash cans, lanterns, wheelbarrows and many objects consisting of several connected together, such as the birds' baths and fountains.
Finding the volume of a cone or pyramid is an excellent mathematical exercise and requires a calculator or a good knowledge of the time tables. If you imagine a prism, a surrounding cone or a pyramid, and the same height, the volume is always one third of the volume of the prism, which gives the formula V = base area x height 3 3.
You can find the volume of a truncated cone or pyramid using a more complex formula, but at the GCSE level, it is best to find the volume of the full form, and then subtract the volume of the part to be deleted.
