The front, side, and bottom faces of a rectangular solid have areas of 
square centimeters, 
square centimeters, and 
square centimeters, respectively. What is the volume of the solid, in cubic centimeters?
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The correct answer is A.
One way to determine the volume of the solid is to determine the length 
, width 
, and height 
of the solid, in centimeters, and then apply the formula 
to compute the volume. Let , , and represent the length, width, and height, in centimeters, respectively, of the solid. The area of the front face of the solid is 
square centimeters, the area of the side face is 
square centimeters, and the area of the bottom face is 
square centimeters. Elimination of by using the first two equations gives 
, which simplifies to 
, or 
. Substitution of 
for in the third equation gives 
, or 
, so 
(since only positive values of make sense as measurements of the length of any edge of a rectangular solid). Substitution of 
for in the equation gives 
, and substitution of for in the equation gives 
, so 
. Therefore, the volume 
of the solid, in cubic centimeters, is 
.
Alternatively, one can recognize that the square of the volume of a rectangular solid is the product of the areas of the front, side, and bottom faces of the solid. That is, squaring both sides of the formula gives 
. Therefore, in this case, 
, so 
. Note that it is not necessary to solve for the values of , , and .