For (a) They tell you dVsphere/dt = KA = 4Kπr2. But you can also find dVsphere/dt by finding d/dt(4/3πr3). You'll wind up with a dr/dt term in that. You can then set the dV/dt equations equal, and rearrange to solve for dr/dt, plugging in 4 for r. You should get for part (a) that dr/dt is a constant number to answer (b). For part (c) find d2V/dt2 and see how that depends on d2r/dt2=0. If d2V/dt2 is 0, then the rate of change of the volume must be a constant, becuase the derivative of a constant is 0
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For (a) They tell you dVsphere/dt = KA = 4Kπr2. But you can also find dVsphere/dt by finding d/dt(4/3πr3). You'll wind up with a dr/dt term in that. You can then set the dV/dt equations equal, and rearrange to solve for dr/dt, plugging in 4 for r. You should get for part (a) that dr/dt is a constant number to answer (b). For part (c) find d2V/dt2 and see how that depends on d2r/dt2=0. If d2V/dt2 is 0, then the rate of change of the volume must be a constant, becuase the derivative of a constant is 0 ( ... )
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