# Truncated cone pattern

Calculates the measurements for the pattern to construct a flat top cone. off any radius, and then measure an angle of 200 degrees. by cutting off a cone with a base having a diameter of 8 inches. in the figure because they will be useful later. The completed cone looks like the figure at the right. to lay out flat is cut from a circular disc of radius 21.63 inches and. factor to get degree measure and you have:. relation for the right triangles, we can determine the lengths. Using the small circle with radius of 7.21 and arc length of, we have. the conical figure up to a point. That is, this pedestal is formed. We can set this up using either the small circle or the large one. of the whole cone and h is the altitude of the little cone. Now, First, h. We have h + 12 is the altitude. of h, a, and b and then roll the figure out flat. the blue figure and join the two sides together. can be found by using the arc length and. draw a circle of radius 21.63 and a smaller circle of radius 7.21. is how big is the angle from A around to B to get the arc lengths. of the lateral sides of the cones and the pedestal. we remove a piece of a circular disc of radius 7.21 inches (the small. angle we use the relation that the arc length S is given by. altitude of the little cone -- and the altitude of the big cone. A cone, optionally with the top cut off. (In that case, it's called a frustum). Can be used to help create the geometry for a beaker, vase, party-hat or lamp shade. If you'd like a real cone, just use zero for the top-diameter. Tip: do not score or fold the fold line this template to keep seam smooth. I solved for PT and got PT = 16.24", and thus PS = 24 + 14.24 = 40.24". All that remains is to determine the measure of the angle SPV. Automatic - fit page to drawing A4 (210 x 297 mm ) US Letter (8.5 x 11 inch) A3 ( 297 x 420 mm) A4 Landscape (297 x 210 mm ) US Letter Landscape (11 x 8.5 inch) A3 Landscape (410 x 297 mm) Custom: you decide. Question: I need to make a large cone segment. The large end has ID of 57 inches and the small end has ID of 23 inches. The cone is essentially a 45 degree cone (90 degrees at the tip). The sides of the segment are 2 feet long. How do I lay out a flat pattern that will fold into this segment? I need to know radius 1 and radius 2 and the angle the piece must be. I can now see that the "flat pattern" is part of a sector of a circle of radius 40.24". where a is the length of the arc SV, r is the radius PS and theta is the measure of the angle SPV in radians. The length of the arc SV is the circumference of the base of the cone. The base of the cone is a circle of radius 57" so. If you find my work usefull, why don't you. . Draw two concentric circles of radius 40.24" and 16.24". Remove a sector with centre angle of 360 0 -254 o = 106 o and roll up what remains to form the truncated cone. The "flat pattern" will be part of a circle of radius PS so I need that length. I know that TS = 24" so I need to find PT. The triangles PQT and PRS are similar so.