You pour 1000 cm^3 of syrup on the floor at the rate of 50 cm^3/s. The syrup flows in all direction equally - creating an expanding circular area as viewed from above. The high viscosity of the syrup causes the syrup to maintain a constant depth of 0.25 cm, creating a thin cylinder. At what rate is the radius changing with respect to time when the radius is 20 cm?

Question

anonymous · Answer

related rates using derivative of cylinder volume formula, me thinks.

anonymous · Answer

$$\large \frac{dr}{dt}=\frac{\cancel{dV}}{dt} \cdot \frac{dr}{\cancel{dV}}$$

amriju · Answer

dV/dt=50cc..V=volume of cylinder...
so...d(3.14r^2*0.25)/dt=50....V=3.14r^2*h.....h is height thats const...
from herefind dr/dt....that will depend on r itself...so u have dr/dt at r =20...

anonymous · Answer

Volume, V, of cylinder = πr^2h; find dV/dr from this.
dV/dt is given.

baldymcgee6 · Answer

V = pi*r^2*d
1000cm^3 = 2*pi*r*dr/dt * 0.25

Solve for dr/dt, then input r = 20

anonymous · Answer

The 1000cm^3 isn't necessary here since the syrup at r=20 is much less than that.

anonymous · Answer

Besides, when you differentiate, the volume formula, you do not get "1000cm^3 = 2*pi*r*dr/dt * 0.25"
If you solve this for dr/dt, it will be incorrect.

lgbasallote · Answer

i wonder if the asker was just deleting his replies...or these users were doing monologues

amriju · Answer

I am always here to show off...lol

anonymous · Answer

I started answering, then others offered insights, so I offered commentary and additional info and corrections on that.

anonymous · Answer

OP seems to be asleep, though  . ..

lgbasallote · Answer

you see it as offering insights...i see it as racing...same shiz...

anonymous · Answer

? What do you mean, @lgbasallote ?

lgbasallote · Answer

everyone wants to be the right one....everyone wants to get the medal....so they race with others....

anonymous · Answer

Interesting interpretation. Does your cynicism often get you to the correct explanation?

lgbasallote · Answer

my cynicism gets me enemies

anonymous · Answer

Cynicism aside, how would you rate the flow of the conversation in its ability to help the asker get the correct answer?

lgbasallote · Answer

no idea. i'm still in algebra

anonymous · Answer

Very well. Thanks for the input.

anonymous · Answer

good post.
I lol'ed.

fellowroot · Answer

Why do we all want to be right? Its because it makes us better than everyone else. hahahahahaha