Problem 19
CONICAL FLOWER HOLDER
37. The Conical Flower Holder.—The sketch, Fig. 115, shows a flower holder, such as is often carried in stock by florists. The body of this holder is a right cone.
Solid of Revolution.—Any plane surface rotating about a fixed point, or a line, generates a solid. For instance, a rectangle rotating about one of its sides generates a cylinder. A right-angled triangle rotating about its altitude generates a cone. Such a cone is known as a Right Cone or a cone of revolution.
Axis of the Cone.—The line about which the generating surface revolves in forming a solid of revolution is called the axis. It is the shortest distance between the apex (point) and the base, and forms a right angle to the plane of the base.
Elevation of the Cone.—The elevation of the cone, Fig. 116, is drawn in the following manner: Draw a horizontal line four inches long; from the center of this line drop a perpendicular seven inches long. Connect the ends of the four-inch line to the end of the seven-inch line by straight lines. The four-inch line is the Base of the Elevation. The seven-inch line is the Altitude of the Cone. The straight lines connecting the ends of the base and the altitude are the Slant Height lines of the elevation. Complete the elevation by drawing a wire nail, Fig. 116, which is to be "soldered" in after the cone is formed.
Profile of the Cone.—The profile of any cone of revolution is a true circle. This circle may be divided into two equal parts; therefore, it is necessary to draw but one-half of the profile as shown in Fig. 116. This profile is divided into equal parts and each division numbered. Extension lines are carried downward until they meet the base line of the elevation.
Elements of a Surface.—Dotted lines are shown in Fig. 116 running from each intersection of the base, to the apex. These represent imaginary lines drawn upon the surface of the cone. If lines were drawn upon the surface of the cone, until the surface was completely covered, each one of these lines would become a part, or an element, of the surface. Any surface may be regarded as being made up of an infinite number of lines placed side by side, each line being an element of the surface.
