Math CentralQuandaries & Queries


Question from Dan:

How many rolls of stock do I need to buy?
The rolls are 40" wide, 20" roll o.d., 4" core o.d., gauge is 0.008"
I need to cut these master rolls in 6" strips (4" of waste per master roll)
and I need 1,270,500 linear feet of this strip.

Hi Dan.

If you need 1,270,500 linear feet of strip and you are making 6 strips per roll, then you need 1,270,500/6 = 211,750 linear feet of stock.

The area of the annulus (the ring) of stock around the core will determine how much stock you have. This is simply the area of a 20" diameter circle minus the area of a 4" diameter circle. That's 102 π - 22 π = 298.45 square inches.

If we unroll the stock, this area would be the same as a rectangle that is 0.008" thick by the linear inches on the roll. Divide that by 12 to get linear feet.

So there is ( (298.45 / 0.008 ) / 12) = 3108.87 linear feet of stock on each roll.

Since we need 211,750 linear feet of roll, we just divide 211,750 / 3108.87 and get 68.1 rolls.

Stephen La Rocque.

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