Only for real math pros!

[kedaman]

An upside down cone with diameter 10m and height 8m is being filled with water, 0.1 m^3 per minute.

What's the speed the surface raising when the water height in the cone is 4 meter

[Sam Finch]

I make it (48/(250*pi)) * ( ( 192 / (25*pi) )^(-2/3) ) /60
= 5.61296766986877E-04 m/s

about half a centimetre per second

[kedaman]

Hey, I got 2.12E-5 m/s
That's 21 micrometers per second, about 1,2 millimeters/s

Something must have screwed up, either you or me or both got wrong answers, so

did you get this equation for height?
h=2t/(625pi)^(2/3)
and then got the derivate and put in t in it?
I got t=20000pi seconds for h=4

[kedaman]

838 m^3 should go in the cone, and if you fill it 0,1m^3 /minute, should take up nearly six days to fill

[Sam Finch]

my bad, I missed out a couple of constants
I got 2.97001026127106E-04 m/s this time, I've done it a completley different way though. I worked out the height in terms of the volume first then found the derivitive and divided by 600

[Guv]

Hey guys, we will never decide what is correct answer without showing how it was derived.

Check the following.

V = Pi*r^2*h/3 (Cone volume in terms of height & radius).

For cone in question, r = 5*h/8

Hence V = Pi*(5*h/8)^2*h/3

or V = 25*Pi*h^3/192

dV = (25*Pi*h^2/64)*dh

dV = (25*Pi*16/64)*dh

dV = (25*Pi/4)*dh

.1 = (19.635)*dh

dh = .1/19.635

dh = .00509 meters/second

I did not recheck all of the above. If you disagree, show me my error. There might be one.

[kedaman]

I'm sorry there was a typo in the qwestion, the radius should be 10m not the diameter. But that won't affect the methods to solve it, thanks for your input Guv :)

[Ianpbaker]

the speed it takes is about the speed it takes arbiter to down a Pint hehehe. sorry just needed to put some humor into this post. back to the assylum I go.