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


Transcript

Example 35 A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm.Let r be the radius of circle . & A be the Area of circle. Given that Radius increases at the rate of 0.05 cm/s Thus, 𝒅𝒓/𝒅𝒕 = 0.05 cm /sec We need to find rate of change of area of circle w. r. t time when r = 3.2 cm i.e. we need to find 𝒅𝑨/𝒅𝒕 when r = 3.2 cm We know that Area of circle = πr2 A = πr2 Differentiating w.r.t time 𝒅𝑨/𝒅𝒕 = 𝒅(𝝅𝒓𝟐)/𝒅𝒕 𝑑𝐴/𝑑𝑡 = π 𝑑(𝑟2)/𝑑𝑡 𝑑𝐴/𝑑𝑡 = π 𝑑(𝑟2)/𝑑𝑡 × 𝒅𝒓/𝒅𝒓 𝑑𝐴/𝑑𝑡 = π 𝒅(𝒓𝟐)/𝒅𝒓 × 𝑑𝑟/𝑑𝑡 𝑑𝐴/𝑑𝑡 = π. 2r . 𝑑𝑟/𝑑𝑡 𝑑𝐴/𝑑𝑡 = 2πr . 𝒅𝒓/𝒅𝒕 𝑑𝐴/𝑑𝑡 = 2πr . 0.05 𝑑𝐴/𝑑𝑡 = 0.1 × πr When 𝒓 = 3.2 cm ├ 𝑑𝐴/𝑑𝑡┤|_(𝑟 =10) = 0.1 × π × 3.2 ├ 𝑑𝐴/𝑑𝑡┤|_(𝑟 =10) = 0.320π Since area is in cm2 & time is in seconds 𝒅𝑨/𝒅𝒕 = 0.320π cm2/s Hence, Area is increasing at the rate of 0.320π cm2/s when r = 0.32 cm

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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.