Question

Use quick estimates (basic assumptions) to find an approximate value for the total area and volume of a piece of paper. Please help!

Answer 1

After 1 layer of paper is wrapped around the core the total length of
paper on the spool, written as L(1), is 2*pi*r, where  r is the radius
of the core, measured in feet.  This is essentially just the
circumference of the core.

After 2 layers, L(2) = 2*pi*r + 2*pi*(r+t), where t is the thickness
of the paper, measured in feet.  This is the first layer from above
plus the second layer, where the second layer is the circumference
around the core and the first layer, making the radius of the second
layer r + t.

After 3 layers, L(3) = 2*pi*r + 2*pi*(r+t) + 2*pi*(r+2t).  This is the
first 2 layers from above plus the third layer, which is now the
circumference around the core and the first two layers, making the
radius of that third layer r + 2t.

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