could someone plz check my work?

Question

The ? is :

1a. what is the mass of the air in a physics classroom that is 8.0 m wide, 10.0 m long, and 2.8 m high?(the mass density of air is 1.29 g/dm^3).

1b. If the mass density of lead is 11.4 g/cm^3, what volume would be occupied by the same mass of lead?


My work: ......since V=WxLxH and D=M/V

1a. 8.0m x 10.0m x 2.8m= 224m^3=V
1.29 g/dm^3= m / 224m^3
1.29 g/dm^3=.00129g/m x 224m^3= 2.9 x 10^-1 is the mass


1b. D=M/V
11.4g/cm^3=2.9 x10^-1g/m^3/V
11.4g/cm^3=.114g/m^3
so .114g/m^3 x V=2.9 x10^-1g/m^3
V=2.9x10^-1g/m^3 / .114g/m^3
V=2.54 g???

Am i right or did i make any mistake in units or calculations anywhere?

Answer 1

(Edward, 1.29 g/dm^3 = 1.29 kg/m^3, and for grams we have to use "g", not "gm")

I will try to correct the step-by-step work:

> 1a. 8.0m x 10.0m x 2.8m= 224m^3=V
> 1.29 g/dm^3= m / 224m^3

Ok so far

> 1.29 g/dm^3=.00129g/m x 224m^3= 2.9 x 10^-1 is the mass

You are converting g/dm^3 to g/m^3 incorrectly, you need to multiply by 1000, not divide (if a dm^3 of a subtance weights N grams, a m^3 must way much more, not much less). Apart from that, the way you wrote it down is not clear, because it says there that 1.29 g/dm^3 is equal to the result (also you forgot the ^3 in one of the terms but I guess that is a typo). You should have written something like:

" I multiply both sides by 224 m^3 therefore:

m = 224 m^3 x 1.29 g/dm^3 = 224 m^3 x 1290 g/m^3 = 288960 g = 288.96 kg "


> 1b. D=M/V
> 11.4g/cm^3=2.9 x10^-1g/m^3/V

You are using a unit of density instead of mass. This line written with the right unit and the correct previous result should read:

11.4 g/cm^3 = 288960 g / V

> 11.4g/cm^3=.114g/m^3
> so .114g/m^3 x V=2.9 x10^-1g/m^3
> V=2.9x10^-1g/m^3 / .114g/m^3
> V=2.54 g???

Well, in any case, it would be 2.54 with no unit, but you were carrying the previous mistake with the unit. There is also no need to convert to m^3. A correct resolution would be:

V = 288960 g / 11.4 g/cm^3 = 25347 cm^3 = 25.347 dm^3

Answer 2

Good work...but


1.The density of air is 1.29 kg/m ^3 (NOT 1.29 g/dm ^3)
So 224m^3 * 1.29 kg/m ^3=288.96kg (Heavy!)
2.V=m/(density of lead)= 288.96kg /11.4 g/cm^3=25347cm^3
(NOT GRAMMS)
This is .025347m^3

Keep in mind
1kg=1000gm=1E10^3
1dm^3=1/1000 m^3=1E10^-3 m^3
1m^3=1,000,000 cm^3 = 1E10^6

Have fun