Example 1 - Find rate of change of area of circle per second - Examples


  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Example 1 Find the rate of change of the area of a circle per second with respect to its radius r when r = 5 cm. We have to find rate of change of area of circle with respect to radius i.e. we need to find ๏ท๐‘‘(๐ด๐‘Ÿ๐‘’๐‘Ž ๐‘œ๐‘“ ๐‘๐‘–๐‘Ÿ๐‘๐‘™๐‘’)๏ทฎ๐‘‘ (๐‘Ÿ๐‘Ž๐‘‘๐‘–๐‘ข๐‘  ๐‘œ๐‘‘ ๐‘๐‘–๐‘Ÿ๐‘๐‘™๐‘’)๏ทฏ = ๏ท๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ We know that Area of circle = ฯ€ r2 A = ฯ€r2 Finding ๏ท๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ ๏ท๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = ๏ท๐‘‘(๐œ‹๐‘Ÿ2)๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = ฯ€ ๏ท(๐‘Ÿ2)๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = ฯ€ (2 . r2 โ€“1) = 2ฯ€ r For r = 5 cm ๏ท๐‘‘๐ด๏ทฎ๐‘‘๐‘Ÿ๏ทฏ = 2ฯ€ (5) . ๏ท๐‘๐‘š2๏ทฎ๐‘๐‘š๏ทฏ = 10ฯ€ ๏ท๐’„๐’Ž๐Ÿ๏ทฎ๐’„๐’Ž๏ทฏ

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