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The guide reviews assumed knowledge and builds motivation using prism volume and surface area formulas, then extends methods to non-uniform solids. 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This work is licensed under the Creative Commons Attribution‑NonCommercial‑NoDerivs 3.0 Unported License. 2011.  \n[http://creativecommons.org/licenses/by](http://creativecommons.org/licenses/by)‑nc‑nd/3 .0/  \nThe Improving Mathematics Education in Schools (TIMES) Project  \nCONES, PYRAMIDS AND SPHERESA guide for teachers-Years 9–10  \nMEASUREMENT AND GEOMETRY Module 12  \nJune 2011  \nPeter Brown Michael Evans  \nDavid Hunt Janine McIntosh  \nBill Pender Jacqui Ramagge  \nYEARS  \n910  \n{4}  A guide for teachers  \nCONES, PYRAMIDS AND SPHERES  \nASSUMED KNOWLEDGE  \n• Familiarity with calculating the areas of the standard plane figures including circles.  \n• Familiarity with calculating the volume of a prism and a cylinder.  \n• Familiarity with calculating the surface area of a prism.  \n• Facility with visualizing and sketching simple three‑dimensional shapes.  \n• Facility with using Pythagoras’ theorem.  \n• Facility with rounding numbers to a given number of decimal places or significant figures.  \n• Facility with manipulation of formulas and equations  \nMOTIVATION  \nIn the earlier module, Area Volume and Surface Area we developed formulas and principles for finding the volume and surface areas for prisms. The volume of a prism,  \nwhose base is a polygon of area A and whose height is h, is given by Volume of a prism = Ah.  \nThis formula is also valid for cylinders. Hence, if the radius of the base circle of the cylinder is r and its height is h, then:  \nVolume of a cylinder = πr2h  \nAlso in that module, we defined the surface area of a prism to be the sum of the areas of all its faces. For a rectangular prism, this is the sum of the areas of the six rectangular faces. For other prisms, the base and top have the same area and all the other faces are rectangles.  \nIn this module, we will examine how to find the surface area of a cylinder and develop the formulae for the volume and surface area of a pyramid, a cone and a sphere. These solids differ from prisms in that they do not have uniform cross sections.  \nThis will complete the discussion for all the standard solids.  \nThe Improving Mathematics Education in Schools (TIMES) Project  {5}  \nPyramids have been of interest from antiquity, most notably because the ancient Egyptians constructed funereal monuments in the shape of square based pyramids several thousand years ago. Conical drinking cups and storage vessels have also been found in several early civilisations, confirming the fact that the cone is also a shape of great antiquity, interest and application. The word sphere is simply an English form of the Greek sphaira meaning a ball.  \nConical and pyramidal shapes are often used, generally in a truncated form, to store grain and other commodities. Similarly a silo in the form of a cylinder, sometimes with a cone on the bottom, is often used as a place of storage. It is important to be able to calculate the volume and surface area of these solids.  \nThe ancient Greeks discovered the various so‑called quadratic curves, the parabola,","cbCaijtBgnUVMI5r","https://ap.wps.com/l/cbCaijtBgnUVMI5r","pdf",2569529,24,"English","# ASSUMED KNOWLEDGE\n# MOTIVATION\n# SURFACE AREA OF A CYLINDER\n## Example: Surface area of each solid","[{\"question\":\"What prior topics do students need for this module?\",\"answer\":\"Students are expected to know areas of standard plane figures (including circles), volumes and surface areas of prisms, how to visualize and sketch 3D shapes, apply Pythagoras’ theorem, round numbers accurately, and manipulate formulas and equations.\"},{\"question\":\"How is the surface area of a cylinder derived in the module?\",\"answer\":\"By rolling the cylinder one revolution, the curved surface traces out a rectangle of width h and length 2πr. The curved area is 2πrh, and adding the two circular ends gives 2πrh + 2πr².\"},{\"question\":\"What solids are introduced beyond prisms in this module?\",\"answer\":\"The module explains how cylinders, pyramids, cones, and spheres differ from prisms because they do not have uniform cross sections, then develops corresponding volume and surface area formulas.\"}]","CONES, PYRAMIDS AND SPHERES - Measurement and Geometry Module 12 - A guide for teachers-Years 9-10 | PDF"]