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March 28, 2015

March 28, 2015

Posted by **rachel** on Sunday, November 6, 2011 at 10:27pm.

so the paper filter is 4 inches tall

whith a radius of 2 inches. x is the height of the water in the cone.

the cup is 4 inches wide and y is the height of the water in the cup. please help! thanks(:

- calculus -
**Steve**, Monday, November 7, 2011 at 12:53pmIf the water in the filter is at depth x, with the surface of radius r,

x/r = 4/2 = 2

x = 2r

r = x/2

now, the volume of the water in the cup, plus that in the filter adds up to 10

cone: v = 1/3 pi r^2 x = pi/12 x^3

cup: v = pi r^2 y = 4pi y

pi/12 x^3 + 4pi y = 10

pi/4 x^2 dx/dt + 4pi dy/dt = 0

multiply by 4/pi to simplify a bit:

x^2 dx/dt + 16 dy/dt = 0

You can massage that into whatever form you need.

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