Ex 6.1, 17 - Rate of change of area of a circle with respect - Ex 6.1


  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Ex 6.1,17 The rate of change of the area of a circle with respect to its radius r at r = 6 cm is (A) 10p (B) 12p (C) 8p (D) 11p Let r be the radius of circle & A be the area of circle We need to find Rate of change of Area of circle w.r.t to radius at ๐‘Ÿ = 6 i.e. we need to find ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ at ๐‘Ÿ = 6 We know that Area of circle = ๐œ‹ ๐‘Ÿ๏ทฎ2๏ทฏ i.e. A = ๐œ‹ ๐‘Ÿ๏ทฎ2๏ทฏ Diff w.r.t ๐‘Ÿ ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ= ๐‘‘ ๐œ‹ ๐‘Ÿ๏ทฎ2๏ทฏ๏ทฏ๏ทฎ๐‘‘๐‘Ÿ๏ทฏ ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ=๐œ‹ ๐‘‘ ๐‘Ÿ๏ทฎ2๏ทฏ๏ทฏ๏ทฎ๐‘‘๐‘Ÿ๏ทฏ ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ=๐œ‹ . 2r ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ=2๐œ‹๐‘Ÿ We need to ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ when ๐‘Ÿ = 6 ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏโ”‚๏ทฎ๐‘Ÿ = 6 ๏ทฏ=2๐œ‹ 6๏ทฏ ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏโ”‚๏ทฎ๐‘Ÿ = 6 ๏ทฏ=12๐œ‹ Hence correct answer is B

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.