You will need

- Pencil, compass, template, triangle, ruler

Instruction

1

Example. To build a

**scan**of a truncated**cone**. The lateral surface of a truncated**cone**has flat elements, because it is a curve surface. To obtain an approximate sweep perform the following construction (figure 1).2

Fill the cone to the polyhedron. On the horizontal projection of the circumference of the bottom base

**of the cone**, divide the arc 12(1₁2₁), 23(2₁3₁), etc. And the circumference of the upper base divide by arcs 67(6₁7₁), 78(7₁8₁), etc., Connect these arcs by chords. The result is written in the truncated cone a truncated octagonal pyramid. Her face is a trapezoid, with the base – chord 1₁2₁, 6₁7₁, etc., and the other two opposite side – the side edges 1₁6₁, 2₁7₁ etc. These facets of the trapeze and are flat elements that are aligned with the plane of the drawing in the scan.3

In every face swipe diagonally 1₁7₁, 2₁8₁, etc., divide them into two triangles. Determine the actual size (N. D.) diagonal 17 by way of a right triangle. To do this, check the height of the front projection of a truncated

**cone**h. At right angles to h put the horizontal projection of the diagonal 1₁7₁. Received 1₀7₁ the hypotenuse is equal to the actual value (B. V.) diagonal 17.4

When building a scanner all dimensions shall be full size. In 1672 faces of the inscribed pyramid all the elements are represented without distortion: the actual value of the rib 16 is equal to its frontal projection 1₂6₂, chord 67 (6₁7₁), 12 (1₁2₁) Proektirovanie in full size on the plane P. The actual value of the diagonal 1₀7₁ found by way of a right triangle.

5

Building sweep. On the vertical straight line (or direct random position) put the cut 1₀6₀=1₂6₂. From the point 6₀ radius 6₁7₁ make a notch, and 1₀ radius 1₀7₁ (present) – the second. The resulting point 7₀ connect direct with 1₀ and 6₀. From the point 1₀ make the notch radius 1₀2₀=1₁2₁, and from the point 7₀ radius 7₀2₀=1₀6₀. Get the point 2₀, connect it to the points 1₀ and 7₀.Built a-line 1₀6₀7₀2₀ is aligned with the plane of the drawing face of the pyramid inscribed in the truncated cone.

6

All the faces of the inscribed pyramid is equal, so using the same dimensions, build all adjacent faces and connect direct point 1₀, 2₀, 3₀, etc. of the Obtained flat figure will scan the lateral surface of the pyramid inscribed in a truncated cone.

7

Connect point 1₀, 2₀, 3₀ etc. the bottom base and the point 6₀, 7₀, 8₀, etc. of the upper base of the truncated

**cone**curved curve line. The resulting figure is a net of a truncated**cone**.Note

In this example, in the drawing, the second half of the sweep symmetrical built and runs similarly on the same size.