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## Algebra 1

### Course: Algebra 1>Unit 3

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.
• 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!
• Why is dividing by seconds the same as multiplying 1/s?
• Because dividing is the same as multiplying by the reciprocal.
• 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.
• The following equation is not from this video but it is same type of problem:

Consider V=IR where I=A and R=kg*m^2/s^3*A^2

(V=A times Kg times m squared divided by (or over) s cubed times A squared)

A(kg*m^2/s^3*A^2)

The answer seems to be Kg*m^2/s^3*A

My question is why does the variable A in the final answer left with no exponents?
• That is because:
A/A² = 1/A
Technically you could see the "A" in the denominator having an exponent of 1, but standard convention is to omit the exponent if it is 1. Comment if you have questions.
• Is saying .6 m is = 60cm? Just curious
• That is correct, metric system allows you to move the decimal, and m to cm (smaller units require bigger numbers) requires decimal move two places to the right.
• what is ^?
• In mathematics, the caret symbol (^) represents an exponent. For example, 2^2 is equal to 4.