How to do this SAT math question?

Question

The front, side, and bottom faces of a rectangular solid have areas of 24 square cm., 8 square cm., and 3 square cm., respectively. What is the volume of the solid, in cubic cm.?

Answer: 24 cubic cm.

Answer 1

3 x 8=24

24/24=1e.g. 24 cu. Cm.

equivalent cube

Answer 2

Let the sides be

X Y Z

X*Y = 24

Y*Z = 8

X*Z = 3

X/Z = 24/3 = 3

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X*Z = 3

X/Z = 3

therefore X=3, Z=1, Y=8

volume = 3*1*8 = 24

Answer 3

The volume of a rectangular polygon is l*w*h.  The issue in this problem is that we need to find these values based on the areas.  We will start by looking at the areas and factoring them.  

24 = 24*1 or 12*2 or 8*3 or 6*4

8 = 8*1 or 4*2

3 = 3*1

Looking at these factors we can easily see that the bottom is 3x1 or 1x3.  It is touching the side piece and the only common factor between them is 1, so we know that the length must be 1 and the width must be 3.  Since the area of the side piece is 8 and 1 is the length, then 8 must be height.  Now just multiply w*h*l = 3*8*1 = 24.