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Is the curved surface area of cone src=/../equations/2009/1/6/67fa91e5-8acb-4eec-96aa-db0255270178.pngRH ???? or is it src=/../equations/2009/1/6/67fa91e5-8acb-4eec-96aa-db0255270178.pngRl ???




src=/../upload/2009/1/6/79cb54a9da20ac1ddda3e6d23e4e57fc_51029.JPG_thumb




Consider a hollow cone of radius (R) and height (H)...to find the surface area of the hollow cone consider a small segment dy at a height y from the top and with a radius r as shown in fig,




now




area of small element dy = 2src=/../equations/2009/1/6/67fa91e5-8acb-4eec-96aa-db0255270178.pngr.dy




integrating to get area of hollow cone




surface area = src=/../equations/2009/1/6/ac593318-af08-4908-839f-dd3713ce4808.png




r=Ry / H (by similarity of triangles)




now carrying out the integration




we get,




surface area of a hollow cone = src=/../equations/2009/1/6/67fa91e5-8acb-4eec-96aa-db0255270178.pngRH = curved surface area




but we know that the curved durface area of a cone is src=/../equations/2009/1/6/67fa91e5-8acb-4eec-96aa-db0255270178.pngrl ..... so how......







PLZ POST COMMENTS....






Amit Saxena , 11 Years ago
Grade upto college level
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