Posted by Rachel | Posted in Coffee and Accessories | Posted on 30-10-2008
Tags: 4 cone white porcelain coffee filter holder, 4 porcelain coffee filter cone holder, coffee, cone coffee filter 4, cotton, filter, shop, shopping
(Calculus: Related Rates)A coffee filter has the shape of an inverted cone. Water is flowing into the filter ?
at the rate of 5 cubic inches per second. If the cone has an altitude of 4 inches and a base radius of 3 inches, how fast is the water level rising when the water is 2 inches deep?
h/r=4/3 ==> r=3h/4
V=πr²h/3=πh(3h/4)²/3=3πh³/16
dV/dt=(9πh²/16)*dh/dt
dh/dt=(16/9πh²)*dV/dt
dh/dt=[16/(9π*2²)]*5=20/(9π) inches per second
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