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14 June, 16:29

If the radius of a sphere is increasing at the rate of 2 inches per second how fast

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  1. 14 June, 16:46
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    You haven't shared all of the question, so I'll guess that you want to find "how fast is the area of the sphere increasing?"

    Area of a sphere = 4*pi*r^2

    Rate of change of area of a sphere with respect to radius r:

    dA/dr = 8*pi*r * (dr/dt)

    Here, that would come out to

    dA/dr = 8*pi*r * (2 inches / sec)

    If you meant, "how fast is the volume of the sphere increasing?" you'd need to use a different equation:

    V = (4/3) * pi) * r^3

    and go through a similar process.
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