When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.01 cm divided by min. At what rate is the​ plate’s

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When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.01 cm divided by min. At what rate is the​ plate’s area increasing when the radius is 41 ​cm?

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Diễm Thu 2 weeks 2021-08-28T17:55:45+00:00 1 Answers 0 views 0

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    2021-08-28T17:56:48+00:00

    Answer: 2.56cm2/min

    Explanation: From the knowledge of deferential calculus,

    Let r = radius (in cm) at time t min

    A = area (in cm2) at time t min

    A = πr2

    GIVEN: dr/dt = 0.01cm/min

    FIND: dA/dt when r =41 cm

    Differentiate the area formula with respect to t:

    dA/dt = π(2r)(dr/dt)

    = π(2(41cm))(0.01cm/min)

    = 82π × 0.01cm2/min

    = 3.142 ×82×0.01

    = 2.56cm2/min

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