I need help with a math problem please!!!?

Update:

If snowball melts so that its surface area decreases at a rate of 1 cm^2/min, find the rate at which the diameter decreases when the diameter is 10cm.

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  • Ash
    Lv 7
    1 month ago

    Surface area of Sphere, SA = πD² ....where D = diameter

    Find derivative with time

    d(SA)/dt = π(2 D) dD/dt

    d(SA)/dt = 2πD dD/dt

    dD/dt = (d(SA)/dt)/(2πD)

    Given d(SA)/dt = -1 cm²/min .... (negative sign shows decrease in rate)

    D = 10 cm

    dD/dt = (-1) /(2π*10)

    dD/dt = -1/(20π)

    dD/dt = -0.016 cm/min

    The diameter of snowball decreases by 0.016 cm/min 

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  • Anonymous
    1 month ago

    Area of a sphere = pi*diameter^2

      

    Take the derivative

     

    dA/dT = 2 * pi * d(diameter)dT

      

    substituting

     

    1 cm^2/sec = 2 * pi * d(diameter)dT

     

    The rate at which the diameter decreases = 0.5 / pi cm^2/sec

     

    I'm a little rusty on this so hopefully it help you to spot any mistakes I've done. 

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  • 1 month ago

    whats your question?

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