Rolls of aluminum foil are 305 mm wide and 0.015 mm thick. What maximum length of aluminum foil can be made from 0.83 kg of aluminum?( d(aluminum)=2.70 g/cm3)

Question

evoker · Answer

Turn the mass into a volume using the density and then use the volume equation to find the length.

evoker · Answer

Though you will need to convert everything so that the units match.

boxman61 · Answer

V=M/D
D=2.70g/cm^3
M=0.83kg

$$\left(\begin{matrix}0.83Kg \ 1\end{matrix}\right)*\left(\begin{matrix}1000g \ 1kg\end{matrix}\right)=830g$$
$$\left(\begin{matrix}830g \ 270g/cm^3\end{matrix}\right)=307.41cm^3$$

evoker · Answer

Looks good so far.

boxman61 · Answer

im stuck here...how do i account for width and thickness?

evoker · Answer

V=LWH

evoker · Answer

Where H would be the thickness

boxman61 · Answer

to confirm
$$307.41=L*305mm*0.015mm$$

evoker · Answer

Not quite once again you will need to do conversions

evoker · Answer

your volume is cm^3 while those measurements are in mm

boxman61 · Answer

$$305mm \rightarrow 305000mm^3 \rightarrow 305cm^3$$
$$0.015mm \rightarrow 15mm^3 \rightarrow 0.015cm^3$$
$$307.41cm^3=L*305cm^3*0.015cm^3$$
L=67.2cm^3

boxman61 · Answer

67.2cm^3 = 4.07 cm = 0.0407meters

evoker · Answer

Conversions appear to be off, we can put it all in cm and cm^3 if you like

evoker · Answer

to go from mm to cm you would divide by 10.

evoker · Answer

and then you can leave the volume alone

boxman61 · Answer

so 305mm /10 =30.5cm
and 0.015mm /10 = 0.0015cm

evoker · Answer

Yes

boxman61 · Answer

307.41cm^3 = 6.75cm

6.75=L*30.5*0.0015    L=147.54cm or 1.48 Meters

evoker · Answer

you can leave the volume as it is, it is  already in cm^3.

evoker · Answer

307.41=L*30.5*.0015  where L will be in cm

boxman61 · Answer

answer needs to be in meters so wouldn't i need to convert the cm^3 to cm?

evoker · Answer

well when you are finished I would convert the length to meters by dividing by 100.

evoker · Answer

You could turn everything to meters but much easier to just solve for L and then convert that answer to meters.

boxman61 · Answer

Oh I see because L W and H are all cm when they multiply the become cm^3
so If I do 307.41=L*30.5*.0015
L=6719.34

evoker · Answer

Yes

boxman61 · Answer

67.2 meters

evoker · Answer

Looks good

boxman61 · Answer

Whew... thank you very much for sticking with me on that one. I really appreciate it

evoker · Answer

No problem, all the conversions do make it a bit tricky