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Ex 6.1, 1 - Find rate of change of area of a circle with respect - Ex 6.1

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Ex 6.1,1 Find the rate of change of the area of a circle with respect to its radius r when (a) r = 3 cm (b) r = 4 cm Radius of circle = ๐‘Ÿ & let A be the area of circle We need to find rate of change of Area w. r. t Radius i.e. we need to calculate ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ We know that Area of Circle = ๐œ‹๐‘Ÿ๏ทฎ2๏ทฏ 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)๏ทฎ๐‘‘๐‘Ÿ๏ทฏ๏ทฏ ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = ๐œ‹ 2๐‘Ÿ๏ทฏ ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = 2๐‘Ÿ ๐œ‹ โ€ข when r = 3 cm ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = 2rฯ€ Putting r = 3 cm ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ๏ทฏ๏ทฎ๐‘Ÿ = 3๏ทฏ= 2(3) ฯ€ ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ๏ทฏ๏ทฎ๐‘Ÿ = 3๏ทฏ = 6 ฯ€ Since Area is in cm2 & radius is in cm ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = 6ฯ€ ๐’„๐’Ž๐Ÿ๏ทฎ๐’„๐’Ž๏ทฏ Hence Area is increasing at the rate of 6ฯ€ cm2/ cm when r = 3 cm (ii) r = 4 cm ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = 2rฯ€ Putting r = 4 cm ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = 2(4)ฯ€ ๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = 8 ฯ€ Since Area is in cm2 & radius is in cm ๐’…๐‘จ๏ทฎ๐’…๐’“๏ทฏ = 8ฯ€ ๐’„๐’Ž๐Ÿ๏ทฎ๐’„๐’Ž๏ทฏ Hence Area is increasing at the rate of 8ฯ€ cm2/cm when r = 4 cm

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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