Question

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 architect’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?

Answer 1

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.

Answer 2

Ok

Answer 3

The tricky part is trying to represent this algebraically.

Answer 4

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

Answer 5

What are the values.

Answer 6

Sorry i fail at math so bad.

Answer 7

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.

Answer 8

Ok

Answer 9

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?

Answer 10

Yeah i understand

Answer 11

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.

Answer 12

Ok Yeah im following

Answer 13

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

Answer 14

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

Answer 15

Whats that?

Answer 16

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.

Answer 17

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

Answer 18

Ok yeah

Answer 19

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.

Answer 20

The answer is 15 ft ?

Answer 21

Yep

Answer 22

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

Answer 23

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

Answer 24

so 15/72

Answer 25

i got 2.5 inches.

Answer 26

sorry...got mixed up between inches and feet

Answer 27

Oh

Answer 28

rather (12*15)/72

Answer 29

Yeah so i was correct.

Answer 30

Yep

Answer 31

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

Answer 32

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

Answer 33

Oh
thanks for your help.

Answer 34

Your in college?

Answer 35

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

Answer 36

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

Answer 37

thanks