SOLUTION: The area of the top of a rectangular box is 252 in2, the area of the front of the box is 105 in2, and the surface area of the box is 834 in2. What is the volume of the box?

Let x, y and z be the dimensions of the box.


Then the top and the bottom both (each) have the area xy = 252 in^2;

     the front and the back both (each) have the area yz = 105 in^2;

     and the two other opposite side faces have the area  xz =  = 60 in^2, each.


NOW

    the square of the volume of the box is


        V^2 = (xy)*(yz)*(xz) = 252*105*60 = 1587600.


    Hence, the volume itself is the square root from this value  V =  = 1260 cubic inches.

As you see, the solution is entirely build on using this trick  

    +--------------------------------------------------------------------------+
    |                                                                          |
    |  the square of the volume = the product of the areas of the three faces. |
    |                                                                          |
    +--------------------------------------------------------------------------+


If you know the trick (as you learned it now, after my explanations),

you will be able to easily solve any similar problem.