Minimum force necessary to push out a cork

[drunknfox]

Homework Statement

2 arms of a u-tube are not identical, one having twice the diameter of the other. a cork in the narrow arm requires a force of 16n to remove it. the tube is filled with water and the wide arm is fitted with a piston. the min force that must be applied to the piston to push out cork is?

Homework Equations

p=f/a

The Attempt at a Solution

p1=f1/(pi*r^2), p2=f/pi*2r^2, p1=p2, f1/(pi*r^2)=f2/(pi*2r^2)...f2=(pi*r^2)*f1/(pi*r^2) which gives me 32. The answer is actually 64. What am i missing?

 

[tiny-tim]

hi drunknfox!

(have a pi: π and try using the X² icon just above the Reply box )

p1=f1/(pi*r^2), p2=f/pi*2r^2, p1=p2, f1/(pi*r^2)=f2/(pi*2r^2)...f2=(pi*r^2)*f1/(pi*r^2) which gives me 32. The answer is actually 64. What am i missing?

it isn't π*2r²

(and using a dimensional argument would be much quicker, and less likely to lead to a mistake)