The sphere is a three-dimensional analogue of the circle. The sphere is a smooth surface that bounds a given volume using the smallest surface area, just as the circle bounds the given area using the smallest perimeter. The sphere is an example of what mathematicians call a minimal surface. These conic sections, as they are also called, all occur in the study of planetary motion. Of these, the parabola, obtained by slicing a cone by a plane as shown in the diagram below, is studied in some detail in junior secondary school. The ancient Greeks discovered the various so-called quadratic curves, the parabola, the ellipse, the circle and the hyperbola, by slicing a double cone by various planes. It is important to be able to calculate the volume and surface area of these solids. Similarly a silo in the form of a cylinder, sometimes with a cone on the bottom, is often used as a place of storage. The word sphere is simply an English form of the Greek sphaira meaning a ball.Ĭonical and pyramidal shapes are often used, generally in a truncated form, to store grain and other commodities. 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. Pyramids 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. This will complete the discussion for all the standard solids. These solids differ from prisms in that they do not have uniform cross sections.
VOLUME OF A HEXAGONAL PRISM WITH HEIGHT AND RADIUS HOW TO
In 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. For other prisms, the base and top have the same area and all the other faces are rectangles. For a rectangular prism, this is the sum of the areas of the six rectangular faces. Hence, if the radius of the base circle of the cylinder is r and its height is h, then:Īlso in that module, we defined the surface area of a prism to be the sum of the areas of all its faces. This formula is also valid for cylinders. The volume of a prism, whose base is a polygon of area A and whose height is h, is given by
In the earlier module, Area Volume and Surface Areawe developed formulas and principles for finding the volume and surface areas for prisms.
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