Finding volume

Sweetdaisy186 said:
What is the volume of a 117 cubic inch box in ml? (1 in = 2.54 cm)
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Really Strong Hint:

117 in<sup>3</sup> * (2.54 cm / 1 in)<sup>3</sup>*(ml / cm<sup>3</sup>)

Do you know where all that stuff came from?
 
Have you a chapter, topic, or index entry on "Dimensional Analysis"? That would be very useful.

The basic idea is to multiply by various versions of unity untill you get what you want. Keep the units straight and you are on your way. Just for an example, I ALWAYS forget how many miles in a 10 km race.

10 km

I don't remember a conversion from km to miles, so I have to break it down to a conversion I do know.

I know that 1 km = 1000 m

10 km * (1000 m / 1 km) = 10*1000*(km/km)*m = 10000 m

That factor was unity, since the two quantities are equal.

I know that 1 m = 100 cm

10000 m*(100 cm / 1 m) = 10000*100*(m/m)*cm = 1000000 cm

I know that 1 in = 2.54 cm
I also know that 1 ft = 12 in

1000000 cm*(1 in / 2.54 cm)*(1 ft / 12 in) = [1000000/(2.54*12)]*(cm/cm)*(in/in)*ft = 32808.3989 ft

Lastly, I always remember that 1 mi = 5280 ft

32808.3989 ft * (1 mi / 5280 ft) = [32808.3989/5280]*(ft/ft)*mi = 6.213712 mi

In your case:

117 in^3

We are given 1 in = 2.54 cm, but we have in^3, so we need this one three times. We know also that cm^3 = ml.

Making any more sense?
 
Thanks! That was a wonderful explaination. We got 1917.286 is that right? Thanks again for all of your help!
 
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