Thursday

July 24, 2014

July 24, 2014

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.

**Related Questions**

calculus - water is poured into a conical paper cup so that the height increases...

Calculus(answer needed immediatly,thanks) - A paper cup has the shape of a cone...

Physics - 7. A plastic cup, 15.0 cm in height, is filled to the rim with water. ...

Science - Thanks for everything guys! This really helped! But I have another ...

science - A test liquid has a density of 1.1 g/ml. When you pour some of it into...

Calculus - If water is poured into a cup at a rate of 1 cubic centimeter per ...

MATHS STATISTICS - B. A soft-drink vending machine is supposed to pour 8 ounces ...

calculus ( related rates ) - a paper cup in the shape of a cone has a diameter ...

Calculus - A leaky cylindrical oilcan has a diameter of 4 inches and a height of...

calculus - Water is pouring into a conical vessel 15cm deep and having a radius ...