SOLUTION: Is it possible for two containers with equal surface areas to be completely filled with different amounts of liquid? Explain.

Yes indeed.  If you fill a flimsy paper cup completely full of water and then
squeeze the sides of the cup making it oval shaped, what will happen?  It will
overflow, right? Why?  You didn't change the surface area when you squeezed it,
did you? No.  But the squeezed paper cup will not hold as much water as the
unsqueezed one, yet the surface area of the squeezed cup is exactly the same as
the surface area of the unsqueezed cup.  

Here is a better illustration.  Look at these two boxes:



BOX A and BOX B have the same surface area.  Here is why:

BOX A:

The front rectangle has area 3in x 6in or 18in²
The back rectangle also has area 3in x 6in or 18in²
The rectangle on the left has area 2in by 6in or 12in²
The rectangle on the right also has area 2in by 6in or 12in²
The bottom rectangle has area 3in by 2in or 6in²
The top rectangle also has area 3in by 2in or 6in²

So the surface area of BOX A is 

18in²+18in²+12in²+12in²+6in²+6in² = 72in²

BOX B:

The front rectangle has area 2in x 8in or 16in²
The back rectangle also has area 2in x 8in or 16in²
The rectangle on the left also has area 2in by 8in or 16in²
The rectangle on the right also has area 2in by 8in or 16in²
The bottom rectangle (a square) has area 2in by 2in or 4in²
The top rectangle (also a square) also has area 2in by 2in or 4in²

So the surface area of BOX B is 

16in²+16in²+16in²+16in²+4in²+4in² = 72in² 

So the total surface area of both boxes is the same, 72in²

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However their volumes (how much they will hold) is different.
Here is why:

The volume of BOX A is 

V = LWH = 3in x 2in x 6in = 36in³ 

The volume of BOX B is 

V = LWH = 2in x 2in x 8in = 32in³

So the two boxes have the exact same surface area but
BOX A holds 4in³ more than BOX B. 

Edwin