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24 April, 03:50

When a circular plate is heated in an oven, its radius increases at the rate of 0.01 cm/min. At what rate is the plate's area increasing when the radius is 50cm? Be sure to include units in your answer.

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  1. 24 April, 06:27
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    3.14 cm²/min

    Step-by-step explanation:

    rate of increasing of radius, dr/dt = 0.01 cm/min

    r = 50 cm

    Area of plate, A = πr²

    rate of increase of area

    dA/dt = 2πr dr/dt

    dA/dt = 2 x 3.14 x 50 x 0.01

    dA/dt = 3.14 cm²/min

    Thus, the increase of rate of area is 3.14 cm²/min.
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