   SEARCH HOME Math Central Quandaries & Queries  Question from shailesh: Dear Sir, How can i estimate weight of paper tube from size. i have paper tube inner diameter : 22mm, thickness : 2mm, length : 14mm. so how can i got weight of paper tube? Hello Shailesh,

The information you are given is sufficient to calculate the volume of paper used to make the tube.(Can you see how? Write back if you need help.) To convert from volume to mass, you need to know the density of the paper from which the tube is constructed.

Tyler

Shailesh wrote back

Dear Sir,
How can i estimate weight of paper tube from size. i have paper tube
inner diameter : 22mm, thickness : 2mm, length : 14mm., GSM of Paper : 180
so how can i got weight of paper tube?

Shailesh,

If you sliced the tube from end to end and rolled it out flat you would have a rectangular piece of paper 14 mm long and width the circumference of the tube. The circumference of a circle is π times the diameter so the rectangular sheet of paper would have an area of

14 × π × 22 = 967.61 sq mm.

Since there are 1,000 millimeters in a meter there are 1,000,000 square millimeters in a square meter. Hence the rectangular sheet of paper would have an area of

967.61/1,000,000 = 0.00096761 sq m.

at 180 grams per square meter that's

0.00096761 × 180 = 0.174 grams.

If you have other tubes and the dimensions are in millimeters and grams per square meter then the procedure to calculate the weight of the tube is as follows:

S = (length × π × diameter)/1,000,000 is the surface area in square meters and then
W = S/(GMS of paper) is the weight in grams.

I hope this helps,
Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.