*14. The figure represents in plan and elevation a pyramid with a square base EFGH, and vertex V, standing on a cylinder, ABCD in plan, height AA2. The solids are intersected by a vertical plane whose trace is the shaded line KL. Show the intersection set up from a ground line x2y2, parallel to KL, and seen in the direction of the arrow. Show, also, the portions of the solids visible behind the plane of section. Shade the outline of the section. 15. Draw the plan of a regular tetrahedron, the apex of which is 2 inches above the base, which rests on the horizontal plane. *16. Draw the sections of the given solids made by the vertical plane of which LM is the horizontal trace. Show also the elevation of the portions of the solids visible beyond the plane of section. *17. The projections of a solid are given. Draw the true form of the section of it made by a vertical plane of which mn is the horizontal trace. Show also in elevation the portions of the solid seen behind the plane of section. The edges of the section may be shaded. 18. Draw the projections of a regular octahedron of 2 inches edge, resting with one face in the horizontal plane. The xy line makes an angle of 25° with one edge of that face. 19. A right pentagonal prism (side of pentagon 2 inches) 4 inches long lies with one long edge in the horizontal plane, and one face containing that edge inclined at 30° to the horizontal plane. Draw its plan; also an elevation on a vertical plane, which makes an angle of 60° with each of the long edges. 20. The axis of a right cylinder of 1 inch radius is inclined at 40° to the horizontal plane. Draw the true form of a horizontal section through it. *21. The rectangle ABCD is the base of a pyramid, resting on the horizontal plane. If V be its vertex, the inclinations of the triangular sides to the horizontal plane are as follows:-AVD 50°, AVB 70°, BVC 55°. Complete the plan of the pyramid. A B D C HORIZONTAL PROJECTION. *1. A plane is represented by a scale of slope, the unit for heights being 0.1 inch. A point A in the plane is shown by its plan a :-(a) Draw the horizontal trace of the plane. Draw also the plan of a horizontal line lying in the plane and containing A. (b) Measure the height of A and index its plan ɑ. (c) If the plane were turned into the horizontal plane about its horizontal trace, show where the point A would be carried to, labelling this point A。. inch to *2. The plan of a piece of ground is shown to a scale of 100 feet. The form of the surface is indicated by horizontal sections or contour lines, at vertical intervals of 100 feet. A portion of the surface is seen to be plane. Draw the plan of any path of steepest slope up this plane. Find and measure in degrees the inclination of this path to the horizontal. Represent the plane by a scale of slope. *3. The diagram shows the plan of a portion of a room drawn to a scale of 1 inch to 10 feet. O is one corner of the floor. P is a point 7.3 feet above the floor, shown by its figured plan p.3 (indexed in feet). Determine and measure in feet the distance of P from the corner O of the floor. Find also and measure the distance of P from the line OA on the floor. 0 P7.3 A 4. On the face of a hill a path going North has an upward slope of 1 vertical in 5 horizontal. A path from the same point going East has an upward slope of 1 in 7. Determine and measure the direction (in degrees East of North), and the slope, of the steepest path up the hill. *5. The figured plans of two lines rs, st are given. Determine the plan of the bisector of the angle rst. Show the point where this bisector meets the horizontal plane. Unit = : 0.1 inch. ро s 29 t 5 |