Problem!

[saracen098]

Sugar is leaking out of a container in a cone pile on the floor.Italways has a base width of 1.8x theheight. If theradius of the pile is increase at rate of 2.5cm/when the base radius is 80cm, at what rate is the sugar leaking out of the container.?

[bobbinwales]

2cm ... is that per second?
Sorry don't know that math

[bhg481]

There is a formula for the volume of a cone when the height and radius of the base is known; use this formula to calculate the volume of the cone when the base radius is 80cm. 1 second later the base radius is 82.5cm; work out the new volume and that gives you the increase in volume of sugar in 1 second, which is what you are looking for.

[davebro]

I use Hermesetas.

[10ClarionSt]

Errrrrm, gradually?

[Peter Pedant]

well done bhg - good answer,
I was doing all h's and l's ( and r's) and getting into a bit of a mess with the differentials

[Peter Pedant]

hey clarion
maff ability is linearly related as one goes up Oldham road.
starting at Clarion St as er low, and passing Church st.,
what level is someone living in Failswworth? b) motorway interchange

[Peter Pedant]

it doesnt matter about the unit of time

[bhg481]

Peter is absolutely right. I assumed 1 second because that's the unit used in most exam maths problems but it could just as well been 1 minute or 1 hour etc; the answer would than be in sugar/minute or sugar/hour etc.

[Etch]

bhg481's method doesn't give the exact mathematical answer, because the rate of increase of the volume of the cone is not linearly dependent on the rate of change of the radius of the cone base. You can see this if you calculate the change in volume after an increase of 5.0cm and divide by 2 (time units). The exact answer involves differentiating the formula for the volume of the cone as a function of the base radius.

[bhg481]

Etch - quite right. We don't know the level of the exam question. I gave the "O" level solution, the "A" level solution will involve calculus.

[bobbinwales]

Well my calcs say its leaking very fast so I must of gone wrong as I get around 56000 cubic cms per second!

[Peter Pedant]

excuse me sir!
80 and 2.5 means you can use the principle (short cut) of infinitesimals
I suppose 1% wd be better. I am more army or engineering than Hawking

[archibaldy]

Sugar would also likely begin to stick to the hole in the container due to humidity in the air so over time the outflow rate would likely slow and possibly even stop

[bobbinwales]

Mine looks OK of its all in terms of per hour.
Has anyone did the calc as no ones put an answer??

[bhg481]

I don't do people's homework for them; I just try to teach them the method to help them learn. Hence I didn't even provide the formula for the volume of a cone - it's down to them to look it up as part of the learning curve.

[bobbinwales]

OK but dosnt help me know if am doing it right or wrong... never to old to learn

[bhg481]

bobbinwales - OK, show me your working and I'll tell you whether you are right or not and, if applicable, where you went wrong.

[bobbinwales]

Well I give my answer earlier.. around 57000cc's per whatever time unit is. If its right or clearly wrong maybe just say so and if no ill try again. Would take me ages to show working on here

[Etch]

bobbinwales - the values you have quoted are 'in the right ball park' compared with the mathematical solution, and bhg481's method. Which method have you used?