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22 February, 09:34

Assume that the radius r of a sphere is expanding at a rate of 40 cm/min. The volume of a sphere is

V = 4/3πr^3 and its surface area is 4πr^2. Determine the rate of change in surface area when r = 10 cm.

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  1. 22 February, 09:42
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    S = 4pir^2

    dS / dt = [dS / dr] * [dr/dt]

    dS / dr = 8pir

    r = 10 cm

    dr / dt = 40 cm/min

    => dS/dt = [8pir]*40cm/min

    => dS = [8pi*10cm]*40cm/min = 10,053 cm^2 / min

    Answer: 10,053 cm^2 / min.
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