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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

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 π = 22/7) Now, 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 = 2𝜋𝑟2 = 2 ×22/7×(3.5/2)^2 So, Radius = r = (𝟑.𝟓)/𝟐 Surface Area of Hemisphere = 2𝜋𝑟2 = 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 = 𝜋𝑟𝑙 Here, Radius = r = (𝟑.𝟓)/𝟐 = 1.75 cm And, Height of cone = Height of top – Radius of hemisphere = 5 – 1.75 = 3.25 cm We find 𝑙 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 We find 𝑙 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 Now, Curved Surface area of cone = 𝜋𝑟𝑙 = 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.