How much tar paper?

My dad got a partially used role of tar paper and wanted to know how many square feet it has left.

The roll is 36.0 in. wide, with a 6.00 in. diameter.  The hollow core of the roll has a 2.88 in. diameter, and the tar paper is 0.02 in. thick.

Is there enough to cover 4 faces of an 8-ft. cube?

I like this problem because it can be solved in at least two ways.  What is the answer?


  1. ... with about 16 square feet left over.

  2. Cool - did you do it a simple way or a complex way?

  3. depends on where you draw the line between simple and complex ....

    The number of layers on the roll is (6-2.88)/2/0.02 = 78
    Average diameter of each layer is (6+2.88)/2 = 4.44"
    Therefore average circumference of each layer is pi*4.44"
    so the total length on the roll is pi*4.44*78 = 1087.44
    Area of the paper on the roll is 1087.44*36 = 39148 sq.ins or 271.86 sq.ft

    We need 8*8*4 = 256 sq.ft to paper 4 sides of the cube.

    So assuming no overlapping, we have enough on the roll with 15.86 sq.ft left over.

    I have assumed that each layer on the roll is circular rather than spiral-shaped (is there a word for spiral shaped?), which I believe is fair and in any case this assumption will lead to an under-estimate of the quantity on the roll.

  4. Wow - this is a third way! I'm a little confused about how you go the "average diameter" though.


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