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24 December, 15:48

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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  1. 24 December, 16:11
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    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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