i need to figure out how to calculate the cabinet dimensions using the Vb (from cubic in.)
You mean from cubic inches to cubic feet, or to arrive at the dimensions for each side?
1728 cubic inches in a cubic foot (12" x 12" x 12") and 28.3 liters in a cubic foot.
If you know how many cubic inches in the Vb, divide that number of by whichever dimension is most important, then divide what's left over by the next most important dimension. The remaining number will be the last dimension.
Ex., 1.3ft³ = 2246.4 in³
If the cabinet width will be 12", you'll divide:
2246.4/12=187.2
If you want the height to be 22",
187.2/22=8.5
8.5" will be the depth, for a cabinet that's 12"W x 22"H x 8.5"D
If you want to use the Golden Ratio for the box proportions, you need to find the cube root of the volume (this will be the dimension for one side, let's call it Side A) and divide by 1.618 (this is close enough for this purpose). Side C will be found by multiplying the cube root by 1.618. This method assumes that we aren't using a scientific calculator. Since we know the internal volume for a 1.3ft³ box isn't much more than 1ft³, we can start with a dimension that's just more than 12" as a starting point. Then, you go a bit higher until you're close enough to the total in cubic inches.
12.1 x 12.1 x 12.1 = 1771.561 in³, which isn't large enough.
13 x 13 x 13 = 2197 in³, which still isn't large enough but it's close.
13.2³ = 2299.968, which is a bit more than 2246.4, so we reduce it slightly.
13.1³ = 2248.091 in³
Then, using 13.1 for Side A, Side B will be found using 13.1"/1.618=8.1" and Since C will be found using 13.1x1.618 =21.19"
This a bit over-sized, so rounding down will get you closer to the actual volume.
