The lengths of the radius and height of circular cylinder are changing with time

Question

The lengths of the radius and height of circular cylinder are changing with time. At the time in equation, r = 5 cm, h = 9 cm, dr/dt = 0.2 cm/sec, and dh/dt = 0.4 cm/sec. At what rate is the volume changing at that instant. The lengths of the radius and height of circular cone are changing with time. At the time in question r = 3 ft, h = 10 ft, dr/dt = 0.1 ft/sec and dV/dt = 0.3 ft^3/sec. At what rate is the height changing at that instant? The lengths x, y and z of a box are changing with time. At the time in question x = 7 m, y = 8 m, dx/dt = dy/dt = 0.3 m/sec, dz/dt = 0.02, and dV/dt = 1.5 m^3/sec. What is the length of side z at that instant? The voltage V in a circuit that satisfies the law V = IR is dropping as the battery wears out. Currently, R = 800 ohms, I = 0.05 amp, dR/dt = 0.4 ohm/sec, and dV/dt = -0.012 volt/sec. Determine the rate at which the current is changing at that instant.

Explanation / Answer

1. V=pi r2h

dv/dt= pi 2r h (dr/dt)+ pi r2(dh/dt)

dV/dt=pi *90(-0.2) + pi * 25(0.4)

dV/dt=-18pi +10pi =-8pi ft3/sec

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