Question

The radius r of the base of right circular cone is decreasing at the rate of 2cm/min . and its height h is increasing at the rate of 3cm/min . when r = 3.5cm and h = 6 cm ,find the rate of change of the volume of the cone (use π = 22/7)

Answer 1

HEY DEAR ...✌

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The radius r of the base of  right circular cone is decreasing at the rate of 2cm/min
dr/dt=-2
its height h is increasing at the rate of 3cm/min
dh/dt=3
Volume (V) is =1/3pi*r2*h
Take derivative w.r.t t
dV/dt=1/3*pi*(r2*dh/dt+h*2*r*dr/dt)
        =1/3*pi*(3.52*3+6*2*3.5*(-2))
        =1/3*pi*(36.75-84)
        =1/3*pi*(-47.25)
        =-49.4801.



HOPE , IT HELPS ... ✌

Answer 2

The answer for this question is 48.4901. Please mark as brilliant.