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December 21, 2014

December 21, 2014

Posted by **jhon** on Saturday, May 5, 2012 at 3:09am.

- calculus(related rates) -
**Steve**, Saturday, May 5, 2012 at 10:53amYou know, when you posted this earlier, with a typo, my solution should have enabled you to get the corrected answer. I assume you did that, and are now just confirming your subsequent work.

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Right?

when the water is at depth y, the radius r of the surface can be found using similar triangles:

r/y = (6.5/2)/15

r = 13/60 y

at depth y, the volume of water is

v = 1/3 pi r^2 y

= 1/3 pi (13/60)^2 y^3

= 169pi/10800 y^3

dv/dt = -12200+C = 169pi/3600 y^2 dy/dt

at y=1m=100cm, dy/dt = 21cm/min

-12200 + C = 169pi/3600 * 10000 * 21 =

C = 30971

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