SOLUTION: I want to buy a humifier and it states it will cover 16,000 cubic feet. How do I determine the actual size of the room if I know the height is 8 feet tall? What would be the dimens

Question 835503: I want to buy a humifier and it states it will cover 16,000 cubic feet. How do I determine the actual size of the room if I know the height is 8 feet tall? What would be the dimensions length and width?
Ex. I know a room that is 21 feet long by 19 wide by 8 tall would be 3192 cubic feet, but if I started with 3192 cubic feet, how would I convert that into length by width by height?
Thank you.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let's assume the volume is 3192 as you state.
let's assume the height is 8 feet as you state.
divide 3192 by 8 and you are left with 399 square feet.
so you have x * y = 399 square feet.
x is the length and y is the width.
without knowing anything about the length of the width, you would simply have to make a table of the possible combinations that will makie 399 when multiplied by each other.
the combinations could be 1 * 399
they could also be 3 * 133.
they could also be 7 * 57
they could also be 19 * 21
that probably exhausts the possibilities because the next multiple would be 21 * 19 which means we are in the reverse ratio and will just wind down back over the same factors which would be:
21 * 19
57 * 7
133 * 3
399 * 1
now, if the rooms are not exactly the number of feet, then you would have to do more calculations.
suppose the rooms are measured to the half a foot.
that's more calculations.
suppose the rooms are measured to the quarter of a foot.
that'e even more calculations.
there is not one solution to the problem the way you are posing it.
you have lots of combinations that, when multiplied together, will yield an area of 399 square feet.
if you know the ratio of the length to the width, then you can solve it by equation.
outside of that, it's just brute calculations depending on how fine the measurements of the length and the width will be (to the nearest foot, half foot, quarter foot, inch, etc).

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