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Example 1 - Rasheed got a playing top (lattu) as his birthday - Surface Area - Added

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Example 1 Rasheed got a playing top (lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere(see figure). The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take = 22/7) Surface area to colour = Surface Area of hemisphere + Curved Surface Area of cone Surface Area of hemisphere Diameter of hemisphere = 3.5 cm So, radius = r = 3.5/2 Surface Area of hemisphere = 2 2 = 2 22/7 (3.5/2)^2 = 2 22/7 3.5/2 3.5/2 = 11 0.5 3.5 = 19.25 cm2 Curved Surface area of cone Curved Surface area of cone = Here, radius = r = 3.5/2 = 1.75 cm Height of cone = height of top radius of hemisphere = 5 1.75 = 3.25 cm We find first We know that l2 = h2 + r2 l2 = (3.25)2 + (1.75)2 l2 =10.56 + 3.0625 l2 = 13.6225 l = ("13.6225" ) l = 3.69 cm Curved Surface area of cone = = 22/7 3.5/2 3.6 = 11 0.5 3.6 = 19.8 cm2 Hence, Surface area of the top = Surface area of hemisphere + Curved Surface area of cone = 19.25 + 19.8 = 39.05 Hence, area of the top = 39.05 cm2

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.