Someone please check my math work. problem is pretty important

[SnoopCat]

laser printer can print 50lines of 80 characters per page
average character occupies a box 2mm * 2mm
about 25% of which is toner, rest is blank
toner layer is 25 microns thick

printers toner cartridge measures 25 x8 x2cm
how many pages is a toner cartridge good for?














1 cm = 10mm = 10,000 micron


toner cartridge has a volume of 25cm * 8 cm * 2 cm = 400cm^3 of toner
80 characters * 50 lines = 4000 characters per page

Measurements of toner needed per character
0.5mm = 0.05cm (height / width per character)
25 microns = 0.0025cm (for depth per character)

1 character = 0.05cm * 0.05 cm * 0.0025cm = 0.00000625cm^3 of toner

Toner needed per page
0.00000625cm^3 of toner * 4000 chars/page = 0.025cm^3 per page

Pages Possible Per Toner
400cm^3 / 0.025cm^3 = 16,000 pages


supposedly, the answer is 4000pgs, any ideas?

 

[SnoopCat]

none?

 

[rgwalt]

50 lines/page * 80 chars/line * (4/(1000^3)) m^2 page area/char * .25 toner area/page area * 25x10^-6 m height = 1x10^-7 m^3 toner/page.

Vol of a toner cartridge = (25*8*2) cm^3 / (100 cm/m)^3 = 4x10-4 m^3 /toner cartdridge

Pages = Vol / (vol toner/page) = 4x10-4 / 1x10-7 = 4000 pages

Ryan

 

[notfred]

just read the box the toner came in. It'll say how many pages it's good for.

 

[rgwalt]

OK, one more time, step by step:

Characters per page = 50 lines/page * 80 chars/line = 4000 chars/page

Area of one character = 2 mm * 2 mm * (m/1000mm)^2= 4x10^-6m^2 per character

Volume of toner per character = Area of one character * .25 (toner area/character area) * 25 microns height * (1 m)/(1x10^6 microns) = 2.5x10^-11 m^3 toner per character

Volume of toner per page = Volume of toner per character * # characters per page = 1x10-7 m^3 toner per page

Volume of toner cartridge (cm^3) = 25 * 8 * 2 cm^3 = 400 cm^3

Volume of toner cartridge (m^3) = 400 cm^3 * (m/100cm)^3 = 4x10-4 m^3

Number of pages per toner cartridge = Volume of toner cartridge/volume toner per page = 4x10-4 m^3 / (1x10^-7 m^3 toner per page) =
4000 pages

I hope that explains it better. I couldn't follow what you did due to the lack of dimensional analysis. Set up your problem like I did mine. Make sure all your units cancel. Good luck.

Ryan

 

[DuffmanOhYeah]

you obviously forgot to carry the 1.

with the hurting and the screaming and the umglavin....

 

[TuffGirl]

<< Measurements of toner needed per character
0.5mm = 0.05cm (height / width per character)
25 microns = 0.0025cm (for depth per character)

1 character = 0.05cm * 0.05 cm * 0.0025cm = 0.00000625cm^3 of toner >>



I think your calculations are all clear and correct with the exception of figuring out the area of each character. Each character takes up 2mm x 2mm. You figured the toner per character by taking 1/4 of 2mm and then squaring it, rather than getting the area first (squaring the 2mm) and then taking 1/4 of that ...

It should read:

1 cm^2 = 100 mm^2

2mm * 2mm = 4 mm^2 = .04 cm^2 (height * width per character)

1 character = .04 cm^2 * 0.0025cm * 0.25 = 0.000025 cm^3 of toner


You'll see that 0.000025 / 0.00000625 = 4 which is the factor your answer is thrown off by.

I hope this helps!

 

[SnoopCat]

klee thats exactly it
thnaks

 

[TuffGirl]

np, i'm glad i could help!



<-- actually likes algebra