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### Course: Digital SAT Math>Unit 3

Lesson 2: Unit conversion: foundations

# Units — Harder example

Watch Sal work through a harder Units problem.

## Want to join the conversation?

• This is an easier way to do it:

The word problem says that 1meter=3.28feet, but the answer needs to be per cubic meter, so you have to transform 1m=3.28ft in cubic:
(1m)^3 = (3.28ft)^3
1m^2 = 35.3ft^3

Then you just need to multiply 35.3 per 2.1 (max density):
35.3*2.1 = 74.13 ;)
• Me the whole time . . so confused
o
• 1meter-3.28feet
Cube both sides, (since we are asked to leave our answer in computers per cubicmeter)

.:1cubicmeter-35.29cubicfeet

and we were told that the room must not exceed 2.1 computers per cubicfoot, i.e,

2.1computers-1cubicfoot.

now, the question is... how many computers will contain 1cubicmeters and 1cubicmeters is equal to 35.29cubicfeet

so, translating the above we have, how may computers will contain 35.29cubicfeet,

and 2.1coputers-1cubicfoot
xcomputer-35.29cubicfeet (i.e 1cubicmeter)
so, when we cross-multiply, we have x to be equal to 35.29 X 2.1 = 74.10computers per 35.29cubicfeet
= 74.10computers per 1cubicmeter.
• Can you dumb this down for me
• Don't make a diagram!
Except just use this:
1m = 3.28ft
1m^3 = (3.28)^3 = 35.28
Now multiply it with given 2.1 as 2.1 x 35.28 = 74.10
Easy
• shouldn't 3.28^3 be divided by 2.1 in order to see how many computers can fit in, instead of multiplying?
• Ok, so I was looking at Natalie's answer down below and it really helped me to understand. I was gonna copy and paste her answer here, but I didn't wanna take the credit so I think it'd be helpful if you looked at her answer below.
• im confused as to why he multiplied the 3.28^3 with 2.1, can anyone explain why ?
• The 3.28^3 is the volume of the server room in ft^3. He multiplied it by 2.1 because the question states that only 2.1 computers can fit in a cubic foot of the volume.

1 ft^3 = 2.1 computers
3.28^3 or approx. 35.29 ft^3 x 2.1 comp/ft^3 =
approx. 74.10 computers.

The answer is over cubic meters because (3.28^3) ft^3 = (1) m^3 (which is stated in the question itself).
• I get where he got 35.28ft^3 but why did he multiply it by 2.1ft^3 ?
• He's multiplying 35.28ft^3 with 2.1 computers per ft^3, not just ft^3. There's a big difference. By multiplying these numbers, we can get how many computers can be put in 35.28ft^3
• One way to look at this:

Given:
(1ft)^3 = 2.1 ----1
1m = 3.28ft ---- 2

Working:
1ft = (1/3.28)m ---- 2'
[(1/3.28)m]^3 = 2.1 ---- 2' into 1

[1/(3.28)^3]m^3 = 2.1
m^3 = 2.1(3.28)^3
• I don't understand why he multiplied by density?
• Good Question. The density in this problem gives a ratio for the number of computers to cubic feet.One of the reasons he multiplied by the density was to get the units (ft3) to cancel, which leaves the cubic meters by themselves. Also, this method, known as the "factor label method" is a common means on unit conversion, which is what this problem involves (converting computers per cubic foot into computers per cubic meter.