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標題:
Rate of change
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發問:
A right cylinder is changing in such a way that its radius is increasing at 3 cm/min and its height is decreasing at 5 cm/min. At what rate is the volume of the cylinder changing when radius is 10 cm. and height is 8 cm.?
最佳解答:
Volume V of cylinder = πr2h dV/dt = π[2rh(dr/dt) + r2(dh/dt)] dr/dt = 3cm/min dh/dt = -5cm/min r = 10 cm h = 8 cm dV/dt = π[2(10)(8)(3) + 102(-5)] = π(480 – 500) = -20 π cm3/min (-62.83cm3/min) The volume is decreasing at 62.83cm3/min
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