Question
Water flows at the rate of 2000 cibic cm per second into a verical cylindrical tank 120 cm in diameter and 6 m high. How fast is the water level rising?
Answers
oobleck
the cross-section has area 3600π cm^2
2000 cm^3/s ÷ 3600π cm^2 = 5/(9π) cm/s
Or, if you want to use calculus
v = πr^2 h = 3600πh
dv/dt = 3600π dh/dt
2000 = 3600π dh/dt
dh/dt = 5/(9π) cm/s
2000 cm^3/s ÷ 3600π cm^2 = 5/(9π) cm/s
Or, if you want to use calculus
v = πr^2 h = 3600πh
dv/dt = 3600π dh/dt
2000 = 3600π dh/dt
dh/dt = 5/(9π) cm/s
jc
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