# conversion problem of litres into cubic inches

Submitted by Hope on Wed, 08/20/2008 - 19:54

i need help trying to figure out how to convert 1Liter into Cubic inches given that 1L=1cubic decimeter, and 1in=2.54cm

1L * (1000ml / 1L) * (1cm3 / 1ml) * (13in / 2.54cm3) = 61in3

i have another problem but this one gives two different densities.. it says that the solution contains 12.0% sodium hyddroxide by mass with a density of 1.131g/mL.  which would be the same as the other one kinda but then it says sodium hydroxide has a density of 2.130g/mL.  what volume of the solutin in liters must be used in an application requiring 1.00Kg of sodium hydroxide?
why are there two diff densities of sodium hydroxide?

The first density mentioned is describing the density of the solution.  The second is describing the density of pure sodium hydroxide.

1.00kg= 1000g

D = M/V

2.130g/mL = 1000g / x mL

solve for x and convert to liters.

do i convert to liters before or after solving for x? x=469.48g?

A quick but important correction

chrisf wrote:

1L * (1000ml / 1L) * (1cm3 / 1ml) * (13in / 2.54cm3) = 61in3

There is a very important difference in where the exponent is placed, it makes a difference if it is outside or inside the parenthesis, especially if you are using a ti calculator.

(13in / 2.54cm3) implies that 1 in3 = 2.54 cm3

which is not correct

1 in3 is not equal to 2.54 cm3

it should be

(1 in)3 = (2.54 cm)3 which means

1 in3 = 16.3871 cm3

That being said the notation should be

1L * (1000ml / 1L) * (1cm3 / 1ml) * (13in / 16.3871cm3) = 61in3

This is a very common mistake when using units of length cubed in conversions.  The textbooks that I have used from Pearson and McGraw Hill, come with multiple choice text banks in which when these types of questions are given, one of the wrong answers is always the value calculated before cubing the appropriate conversion, thus when the student plugs in the numbers and forgets to cube, the answer that they obtain on their calculator is one of the choices giving them a false sense of correctness.

Yes you have to convert to liters after solving for x.  All you have to do in this case is move the decimal place.