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If a cone is rolled for one complete revolution on 8 plane, surface with apex of the cone hinged at a point then the area, covered by the cone will be a sector of circle which represents, the development of lateral surface of a cone., , The radius of the sector (R) will be equal to the true, length of the generator of the cone and the length of the arc will, be equal to the circumference of the base circle of the cone., , Fig, 1.12 : Cone being opened out, The angie '@ sulbwended by the arc of length equal to the circumference of base circle can be calculated as, follows : i, _= a of the circle of radius R * 99°, 2a, 2am, , = x 360°= "5 x 360°, R, where y = radius of base circle, , R = the tue length of generator, , , , :, , Prob. 63 : A fight circular cone of @ base diameter 50 mm axis height 60 mm has it is base in H.P. Draw the, evelopment of lateral surface (DLS) of cone., , Soin. : [For pictorial view refer Mutticolour Fig. C49}., , To draw the projections of the cone :, , Sep 1s Draw a circle of diameter $0 mm in the TV. Divide the base circle into 12 equal parts as 1, 2 3, , Sc 42 and draw the generators with thin lines as 0-J, 0-2, 0-3 .... , 0-12. .., , a Step 2: Project the F.V. and draw, Poe, the gencrators. Name the generators in the FLV. as 0717 072% 03/.--', , Step 1: To draw, ‘he DLS firs calculate 0 from following fc a, Oa 5360", , Step 2: Take generator o”7’ (true length of the, , generator) as radius and draw the, sector of circle with angle 0 which will, be the DLS of the cone., , Step 3: Divide the are of sector in DLS into 12, , equal parts and name the generators in, DLS as O-1, 0-2, O-3 ...., 0-12., , How to divide the given sector of, circle into 12 equal parts., , (i) By protractor, , If 0/12 = x° if x is a whole number, then divide the sector of a circle |, (DLS) * directly with help of |, , protractor., , (ii) Angle Bisector Method, , (a) Draw the angle bisector of a, sector of circle (DLS) and, obtained two equal sub, i) SECLOTS,, , (b) Further draw the angle, bisector of two obtained subsectors., , (c) After constructing four equal, sub-sectors of DLS with, compass take ///2th division, from T.V. and transfer three, divisions in each sub-sectors, of DLS., , (iii) Trial Error Method, , , , , , With compass take //]2th division from T.V. and transfer to the arc of DLS 12 times. Since the, length of 1/1/2th division of arc is not exactly equal to the required length, therefore the obuuned, arc will be shorter by 1.5% to 2% (approximately) that of the exact arc of DLS, , Line work (in DLS) :, Thick ; Draw the thick object lines for the are J-7 and both O-! generators,, Thin : Draw thin construction lines for all the generators except 0-1., , , , Prob. 84: A right circular cone having diameter ot, , base 40 mm, axis length 60 mm resting on its base on H.P, , is cut by an AIP Inclined at 48° to H.P. and bisecting the axis. Draw the DLS of the cone retaining ne, , portion containing base,, , —cceeaeateeteee COTES SE