The Cone and Related Examples

Many people find the geometry of the cone more difficult than that of the rest of the solids. And very often they are right especially when the geometry is applied to practical problems. Figure 251 is the plan and elevation of a cone and shows how an inclined section through the cone can be developed. There are several different sections that can be obtained by cutting through the solid in various directions. A vertical section on the centre line of the cone will be triangular in shape. A horizontal section through the solid will be circular. An inclined section (as in figure 251) will be elliptical. A cut through the cone, parallel to one of the edges of the elevation (see figure 252) will produce a parabola and a vertical section which is not on the centre line of the solid will be hyperbolic in shape (see also figure 252). Figure 251Figure 252