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

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  1. Chapter 6 Class 12 Application of Derivatives
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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 ﷐𝑑(𝐴𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒)﷮𝑑 (𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑑 𝑐𝑖𝑟𝑐𝑙𝑒)﷯ = ﷐𝑑𝐴﷮𝑑𝑟﷯ We know that Area of circle = π r2 A = πr2 Finding ﷐𝑑𝐴﷮𝑑𝑟﷯ ﷐𝑑𝐴﷮𝑑𝑟﷯ = ﷐𝑑(𝜋𝑟2)﷮𝑑𝑟﷯ = π ﷐(𝑟2)﷮𝑑𝑟﷯ = π (2 . r2 –1) = 2π r For r = 5 cm ﷐𝑑𝐴﷮𝑑𝑟﷯ = 2π (5) . ﷐𝑐𝑚2﷮𝑐𝑚﷯ = 10π ﷐𝒄𝒎𝟐﷮𝒄𝒎﷯

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  • Kuldeep Sohi's image
    The length 'x' of a rectangle is decreasing at the rate of 3cm/m and the width 'y' is increasing at the rate of 2cm/m.find the rates of change of :
    (a)  the perimeter  (b)  the area of the rectangle when X = 8 cm and y = 6 cm. 
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