Teapot

Question:

What is the answer to this teapot container visual puzzle?

I bought 2 teapots,

If teapot A holds 32 cups of tea, about how many cups of tea does teapot B hold?

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

.

.

Solution:

The teapot B can hold 16 cups of tea.

Reason :

In the figure above,

For,

POT A: we can see the delivery end level and top of A is at same level i.e. of line AB. As, reference pressure at any height for a liquid is equal to – {rho*g*h}, where rho = density of the liquid, the g= acceleration due to gravity, h= height above the reference level, (here EF ). As at AB the pressure is same at all points. Therefore, POT A can be filled up to brim without spilling i.e. can hold 32 cups of tea = { rho*g*(a1+a2) }

POT B: We can see the delivery end of B, is not at the same level to the brim of B. Therefore, POT B cannot stay full in steady state. To understand, lets imagine a hypothetical case, in which jug B is full as follows :

pressure at point x = rho*g* hb ; (hb = height of teapot B)

the pressure at point y = rho*g*a2

for static equilibrium, the pressure at x and y should be equal, requiring, “hb = a2″. Therefore this kind of arrangement would unstable. Thus tea would pour out of point y, due to the effective pressure of liquid until, liquid comes and settles at level CD.

Now, as we can see, a2 = (a1+a2)/2 {or nearly equal to. I have used the figure to scale.}, thus, height of tea in pot B would be half of that in A. Since volume of container, (assuming areas of their base’ cross-section is same) = base area * height,

Therefore, amount of tea in B is half of that in A. i.e. 16 cups of tea