When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.04 cm divided by min. At what rate is the​ plate’s

Question

When a circular plate of metal is heated in an​ oven, its radius increases at a rate of 0.04 cm divided by min. At what rate is the​ plate’s area increasing when the radius is 43 ​cm?

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Rose 1 hour 2021-09-12T01:55:50+00:00 1 Answer 0

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    2021-09-12T01:57:32+00:00

    Answer:

    The plate’s area is increasing at the rate of 10.81 cm²/min when the radius is 43 cm.

    Step-by-step explanation:

    The area of a circle is given by the following formula:

    A = \pi r^{2}

    In which the area is measured in cm².

    Its radius increases at a rate of 0.04 cm divided by min.

    This means that \frac{dr}{dt} = 0.04

    At what rate is the​ plate’s area increasing when the radius is 43 ​cm?

    This is \frac{dA}{dt} when r = 43

    A = \pi r^{2}

    Applying implicit differentitation

    We have two variables(A and r), so

    \frac{dA}{dt} = 2r\pi \frac{dr}{dt}

    \frac{dA}{dt} = 2*43\pi*0.04

    \frac{dA}{dt} = 10.81

    The plate’s area is increasing at the rate of 10.81 cm²/min when the radius is 43 cm.

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45:7+7-4:2-5:5*4+35:2 =? ( )