**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

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