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July 23, 2014

July 23, 2014

Posted by **Nathaniel** on Monday, November 28, 2011 at 1:50pm.

Sand is being dumped from a conveyor belt at a rate of 20 cubic ft/min into a pile the shape of an inverted cone whose diameter and height are always the same.

Find the rate of increase of the radius when the pile is 20 ft. high.

Thanks.

- Calculus -
**Steve**, Monday, November 28, 2011 at 2:20pmAs we saw earlier,

v = 1/3 pi r^2 h

Since diameter = height = 2r

h = 2r

v = pi/3 * r^2 * 2r

v = 2pi/3 r^3

dv/dt = 2pi r^2 dr/dt

20 = 2pi (10)^2 dr/dt

dr/dt = 1/(10pi)

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