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Consider a cone of vertical height H (in metres) and base radius R (in metres) which is full with water. The cone, at time t=0, starts to leak such that it loses water at a rate of k m^3 per second. Give an expression for the rate of change of H.

L = (H2+R2)1/2 V = (1/3)πR2(H2+R2)1/2

dV/dt = -k

dH/dt = dH/dV × dv/dt

dV/dH = (1/3)πR2H(H2+R2)1/2

Thus, dH/dt = -3k/(πR2H(H2+R2)1/2) ​​​​​​​​​​​

CE

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