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### Course: Algebra I (2018 edition)>Unit 4

Lesson 2: Appropriate units

# Formulas and units: Volume of a pool

When using formulas to calculate real-world quantities, we need to make sure our units are consistent. In this video, the base area of a pool is given in square meters while its height is given in centimeters. In order to use the formula for volume, we need to convert one of the measurements to units that match the other measurement.

## Want to join the conversation?

• Sal, how did you get s^3 at ? This area was unclear for me.
• He got s^3, because s^2 is s*s, so if you multiply another s it will simplify to s^3
• I thought when you divide by something, you multiply by the reciprocal. when you divided by the seconds, why did you multiply by 1/s instead of the reciprocal s/1?
• The reciprocal of `s/1` IS `1/s`. So, I'm not sure what you mean.
• HOW IS m2.m=m3
• m^2 = m*m
Multiply: m^2*m = m*m*m = m^3

Hope this helps.
• doesn't the formula involve pi or something?
• no because it already gives u the area of the base so u don't need to calculate it
• why did you divide by seconds?
• Instead of writing Joules / s, we write
kg*m^2 / s^2 / s
because kg*m^2 / s^2 = Joules.
Hope this helps!
• I am sure I am confusing myself, but at , Sal says that the volume of a cylinder is b * h. According to Google, the volume of a cylinder is another formula, not the one he mentioned. So what does Sal mean by that?

• Sal's formula assumes you already know the area of the base. The area of the base time height will give you the volume of the cylinder. However, you likely won't know the base, so the more commonly used formula is: Area = (Pi R^2)h
The Pi R^2 calculates the area of the base.

Hope this helps.
• Why is dividing by seconds the same as multiplying 1/s?
• Because dividing is the same as multiplying by the reciprocal.
• Why not just do 4x60
----
100
(1 vote)
• Ok. So, you can't just multiply the 4*60, because they are different forms of measurement, meters and centimeters. There are 2 ways to solve this equation, both of which you need to convert one of the measurements to match the other's. Think of it like this. 'To multiply, the measurements need to be the same.'

What you need to do, however is convert one of the measurements such as 4 meters to centimeters and you will have 400 centimeters.
Then you will be able to multiply 400*60 resulting in 2400.
You will then be able to convert to meters, aka 240/100m or 2.4m

The other way to solve this is a bit quicker. You convert the 60 centimeters to meters giving you 60/100m.
Then you can multiply the two to get 240/100m.
• shouldn't that volume of a cylinder be pi times radius squared times height? why is it only base times height in this situation?
• The base is equal to pi*r^2. Remember, the base of a cylinder is a circle. Which, as you said, is the same pi*r^2
Hope this helps!
Merry Christmas-eve!
(Is that even a thing??)
• Why can't you multiply 4 meters to get 400 cm and multiply 400 cm by 60 cm and divide by 100 instead of doing what Sal did at ?
• The key thing to note is the squared and cubed.
1m = 100cm
1m² = 10,000cm²
1m³ = 1,000,000cm³

4m² = 40,000cm²
40,000cm² * 60cm = 2,400,000cm³
So, 2,400,000cm³ / 1,000,000m³ = 2.4m³

All in all, I think this is a longer way to solve the equation, but still worth trying!

p.s, I wasn't thinking about the exponents properly as well, so thanks for your question which got me thinking! :D