From a cylinder drum containing petrol and kept vertical,petrol is leaking at the rate of 10ml/sec. if the radius of drum is 10cm and height 50cm,find the rate at which the level of petrol is changing when petrol level is 20cm.??
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Taking volume as V, radius as R, height as H:
V = π×R^2×H
dV/dt = π×R^2×dH/dt. (Since R is constant)
Given dV/dt = -10 ml/sec (Negative sign due to leaking) & R = 10 cm
Thus, dH/dt = [dV/dt] / [π×R^2] = -10 / [π×10^2]
= -0.03183.
Thus level is decreasing at the rate 0.03183 cm/sec.
Note: Rate of change of level is independent of petrol level
V = π×R^2×H
dV/dt = π×R^2×dH/dt. (Since R is constant)
Given dV/dt = -10 ml/sec (Negative sign due to leaking) & R = 10 cm
Thus, dH/dt = [dV/dt] / [π×R^2] = -10 / [π×10^2]
= -0.03183.
Thus level is decreasing at the rate 0.03183 cm/sec.
Note: Rate of change of level is independent of petrol level
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