Question

The area of the rectangular faces of the box are shown . What is the volume of the box

Answer 1

Label the 3 distinct sides of the box.  I arbitrarily chose the letters a, b and c.
Use the info about areas as follows:

ab=54 in^2
ac=90 in^2
bc=60 in^2

Here you have 3 equations in 3 unknowns (a, b and c), which is enough info to use to determine a, b and c.  Then the volume of the box is a*b*c.

Example:  bc = 90, but c = 60/b.  You could subst. 60/b for c in the 2nd and 3rd equation, which will eliminate c completely and leave you with 2 equations in 2 unknowns.

Continuing this procedure, I determined that a=9, b=6 and c=10.  Thus, the volume of the box is V = 9*6*10 = 540 cubic inches (answer)