### 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?

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?

The answer is yes.

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

ReplyDeleteCool - did you do it a simple way or a complex way?

ReplyDeletedepends on where you draw the line between simple and complex ....

ReplyDeleteThe 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.

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

ReplyDelete