Question

How do I find the maximum volume of a funnel?

Answer 1

defferientiate the formula for the volume of a funnel

Answer 2

set it to zero

Answer 3

solve for the unknown is the last step ;)

Answer 4

wait no it's not.. then test to see which is max and which is min

Answer 5

a funnel is just a cone and tube...if you have to include that bottom part otherwise it is just a cone...cone formula - (1/3)pi(r)(h) tube formula: pi r^2 h

Answer 6

for a cone shaped funnel the volume is
\[V=\frac{1}{3}\pi r^2 h\]

Answer 7

aaak dropped my r^2 on the cone...

Answer 8

I'm confused...In the problem, there's a wall around the funnel.. I don't know if that really changes the volume..

Answer 9

i don't think she knows calculus, so we're probably confusing her.

Answer 10

Nope, I don't.

Answer 11

but if all you want is the maximum...just plug in the height and radius...I don't think we are getting the whole problem...walls don't effect funnels

Answer 12

That's what I figured...

Answer 13

the wall around the funnel will set the values of the radius and height of the funnel so you need to take that into account

Answer 14

then use the volume formula to get the max volume, using the max values of radius and height, given the wall

Answer 15

that would be a heck of a problem for the wall to effect the funnel your funnel would need to be stretchy...aaak

Answer 16

but also dont forget that we have to account for the velocity and which the wind is creating orhtogonal angles witht the wall

Answer 17

and the surface tension of the stuff in the funnel...

Answer 18

and the temperature lol

Answer 19

Last question on this subject....there's an apothem. Do I also need to take that into account?

Answer 20

yes...use the apothem to get the height of the cone (h in the volume formula) \[l^2=r^2+h^2\] where l is the apothem