An architect is designing a public storage building with two different sized storage units. The ceilings will be 8 feet high for each storage unit.
A) All small storage units will have square floors the volume of each small unit will be 1,800 cubic feet. What will be the dimensions of each of these storage units?
B) The ration of the dimensions in the architectâ€™s drawing to the dimension of the actual small storage unit is 1 inch to 72 inches. How many inches of the architects drawing would represent the actual width of each small storage unit in Part A?

- anonymous

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- anonymous

So a room's volume is its height*its width*its length. We are given the height and the volume, as well as the fact that its width=its length. We can construct an algebraic equation with this information that will let us solve for the length and width.

- anonymous

Ok

- anonymous

The tricky part is trying to represent this algebraically.

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## More answers

- anonymous

We have height*width*length=volume. What do you get when you plug in the known values?

- anonymous

What are the values.

- anonymous

Sorry i fail at math so bad.

- anonymous

That's ok, it just takes practice. So you know the rooms height and volume - its given to you in the question! Those are height=8ft and volume=1800ft^3.

- anonymous

Ok

- anonymous

Lets give these dimensions variable names so that we can better work with them. Lets call x width, y length, and w height. If x (height) = 8, then we have 8*x*y=1800 for our equation. Do you follow?

- anonymous

Yeah i understand

- anonymous

Now we have two unknown variables to solve for, which would be impossible usually except that in this case we have an extra bit of information that will help us. We are dealing with a square room.

- anonymous

Ok Yeah im following

- anonymous

A square room implies width=length! Fabulous, this actually means we are only dealing with one unknown variable now instead of two!

- anonymous

8*x*x=1800 -> 8*x^2=1800!

- anonymous

Whats that?

- anonymous

So since width=length, we have x=y. They are always going to be the same in a square room, so we can choose to use just one or the other.

- anonymous

so instead of 8*x*y, we can write 8*x*x or 8*y*y. I doesn't really matter, because since x=y they are all equal

- anonymous

Ok yeah

- anonymous

So the rest is algebra. You can divide both sides by 8, and take the square root of the left hand side to find your width and length.

- anonymous

The answer is 15 ft ?

- anonymous

Yep

- anonymous

Oh ok. Can you help me on part 2. im not sure if its correct.

- anonymous

And in your second part, the scale implies you divide everything by 72 to bring it into the representative scale.

- anonymous

so 15/72

- anonymous

i got 2.5 inches.

- anonymous

sorry...got mixed up between inches and feet

- anonymous

Oh

- anonymous

rather (12*15)/72

- anonymous

Yeah so i was correct.

- anonymous

Yep

- anonymous

I have Part c and Part D
if your not busy can you take a look it it please?

- anonymous

Mm - wish I could but I've got to get back to studying for 3 math finals!

- anonymous

Oh
thanks for your help.

- anonymous

Your in college?

- anonymous

Yeah...we call it University here in Canada ;)

- anonymous

Oh wow. Your one smart guy, well goodluck on your finals.

- anonymous

thanks

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