Conversion Problem for all you MATH people.?

Question

4GB (GB = 10^9 bytes)
MP3 player dimensions: 32mm X 24mm X 2.1mm

how many bytes of memory are stored in a cube whose sides are 100 micrometers?


so i understand that there is a total of 4.0X10^9 bytes in the entire mp3 player. there is also 10X10^6 micrometers cubed for each cube. i believe i should convert the total volume to micrometers, then divide the total volume by the volume of 1 cube. once i have that value, it should provide the total number of boxes. if that's correct, then i should be able to divide that value by the total number of bytes... but it's not workin' out.

someone please help me =)

thanks skeptik!

i actually already figured it out... i just needed the conversion for meters to micrometers, and calculated 2480.15873 bytes.

thanks though!

Answer 1

I would do it like that:
Focus on the millimeter-micrometer relationship: 1mm = 1000micrometer.
And so the volume of the cube whose side is 100micrometer = 0.1mm is
0.1^3 = 0.001mm^3.
The total volume of the device (at least its memory part) is:
32 x 24 x 2.1 = 1612.8mm^3
4GB/1612.8 = 10^9/1612.8 = ~ 620040bytes/mm^3 =
= 620040 * 0.001 bytes in the cube
= 620.04 bytes
or let's just round it to 620bytes.

Answer 2

From your info, I can't say for sure which part isn't working out (since you didn't say what answer you got), but I do see one problem.

A cube 100 micrometers on a side contains 1*10^6 um^3, not 10*10^6. You've inserted an extra factor of ten in your calculation.

The MP3 player is 32*10^3 X 24*10^3 X 2.1*10^3 cubic micrometers. Which comes out to 1612.8*10^9 cubic micrometers.
4*10^9 bytes divided by 1612.8*10^9 um^3 = 2.48*10^-3 bytes per um^3.

Multiply by the number of um^3 in your cube to get
(2.48*10^-3)*(10^6) = 2.48*10^3 bytes

Did that help?