If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at which the diameter decreases when the diamet

Question

If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm. (Give your answer correct to 4 decimal places.) cm/min

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Kylie 3 days 2021-09-14T19:20:13+00:00 1 Answer 0

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    2021-09-14T19:21:48+00:00

    Answer:

    0.0723 cm/min

    Step-by-step explanation:

    A snowball is spherical, so it’s area is given by the following formula:

    A = 4\pi r^{2}

    The radius is half the diameter, so:

    A = 4\pi (\frac{d}{2})^{2}

    A = \pi d^{2}

    If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate at which the diameter decreases when the diameter is 11 cm.

    This is \frac{dd}{dt} when \frac{dA}{dt} = -5, d = 11

    A = \pi d^{2}

    Applying implicit differentiation:

    We have to variables(A and d), so:

    \frac{dA}{dt} = 2\pi d \frac{dd}{dt}

    -5 = 22\pi \frac{dd}{dt}

    \frac{dd}{dt} = -\frac{5}{22\pi}

    \frac{dd}{dt} = 0.0723

    So the answer is

    0.0723 cm/min

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