[ME statics] Papus' theorem - find required height of cup

[Feodalherren]

Homework Statement

Determine the height h to which liquid should be poured into the cup so that it contacts half the surface area on the inside of the cup. Assume that r=11mm and l= 60mm . Neglect the cup's thickness for the calculation.

Homework Equations

Surface Area = 2πXL

where X is the distance to the center of mass from the axis of rotation and L is the length of the line that is rotating.

The Attempt at a Solution

Link to my solution:

https://www.wolframalpha.com/input/?i=4243.57=2pi(11+((.317h)/2))sqrt(h^2+++(.317h)^2)

 

[NascentOxygen]

Is there a question or something to go with your working?

 

[Feodalherren]

It's in the problem statement. You can't see it?

 

[.Scott]

I followed it up to the "want" (4243.57). Then I expected you to subtract the area of the bottom. I didn't try to follow your math passed that point, but I'm wondering if you took that "free bottom" into account.

 

[Feodalherren]

I added the area of the bottom to the area of the side, then divided that total area by half. The question is kind of ambiguous and I don't know if they want me to account for the area of the bottom or not. I'm assuming yes since they only state "surface area" and the bottom certainly has some surface area.

 

[.Scott]

That gave you the correct target area. ("wanted")
But as soon as you put half a drop into the container, you cover the bottom - and that contributes to your "wanted" area. So, to compute how much you need to take from the sides, subtract the surface area of the bottom from your "wanted" number.