Forgive my ignorance, I am sure there is a better way of asking this question. Here is my problem. I want to take a certain specified volume, stated in terms of cubic feet, and structure it three-dimensionally so that it stands according to specified proportions. I want to know what the measurements of my structure will be when that is done.
Specifically, I want to take 10.089259024 cubic feet and set it up as a structure that stands in proportions of 1x1x3. What are the measurements of my structure, and how do you arrive at the solution?
Please feel free to retag appropriately as I simply want to know the answer and any help is appreciated.
Let $s$ be the short side in your structure, which is then $s\times s\times 3s$.
The volume of your structure is then $$ V = s\cdot s\cdot 3s = 3s^3 $$ So you need to solve $$3s^3 = 10.089\ldots \\ s= \sqrt[3] {\frac{10.089\ldots}{3} } \approx 1.498233 $$ So your structure will be $1.498233\times 1.498233\times 4.494699$ all measurements being in feet.