# calculus

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Water is poured into a conical tank 6m across the top and 8m deep at the rate of 10m/min. How fast is the water level rising when the water in the tank is 5m deep?

• calculus -

radius of water level --- r
height of water level --- h

by ratio:
r/h = 6/8
8r= 6h
r = 3h/5

V = (1/3)πr^2 h
= (1/3)π(9h^2/25)(h)
=3/25)πh^3
dV/dt = (9/25)π h^2 dh/dt
given: when h = 5 , dV/dt = 10
10 = (9/25)π (25) dh/dt
dh/dt = 10/(9π)

check my arithmetic

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