ATAR Notes: Forum

HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Standard Mathematics => Topic started by: Lilabear123 on March 19, 2018, 08:32:55 pm

Title: Confused about converting units of measurement?
Post by: Lilabear123 on March 19, 2018, 08:32:55 pm: Hi!

So i'm really confused about how to convert between units of measurement, e.g.
- from cm -> L
- Cm^3 -> KL
Also, are do those two above have the same theory?

Sorry if my explanation is confusing, i'm really confused!
Title: Re: Confused about converting units of measurement?
Post by: RuiAce on March 19, 2018, 08:51:34 pm: The first one isn't justified, because "cm" is used to measure length whereas "L" is used to measure volume.
$\text{Note that what relates volume measurements in metres-cubed}\\ \text{and litres is the conversion }\boxed{\text{1000 L = 1 m}^3}$
$\text{We note that 1000 litres exactly make up a kilolitre.}\\ \text{Hence, we immediately arrive at}\\ \boxed{\text{1 kL = 1 m}^3}$
$\text{Now, 1 m = 100 cm.}\\ \text{Therefore, upon cubing both sides of the equation,}\\ \boxed{\text{1 m}^3\text{ = 100}^3\text{ cm}^3}$
$\text{Therefore }\boxed{\text{1 kL = 100}^3\text{ cm}^3}\\ \text{implying that 1000000 cubic centimetres make up a kilolitre.}$
i.e. \( 10^{6} \) cubic centimetres make up one kilolitre.
$\therefore \text{If we only have 1 cubic centimetre,}\\ \text{all we have is }10^{-6}\text{ kilolitres.}$

ATAR Notes | SMF © 2014, Simple Machines