Question

a tight roll of paper, as delivered to the printer, is 60cm in diameter, and the paper is wound on to a wooden cylinder 8cm in diameter. the paper is 0.0005cm thick. What length of paper is there in the roll in km?(compare the area of the edge of the paper when rolled with that of the paper when unrolled)

Answer 1

The length of the paper roll in kilometers is 1.04 km.

Remember that 100,000 centimeters equal 1 kilometer.

Data and Calculations:

Diameter of roll of paper with cylinder = 60 cm

Diameter of cylinder for the roll = 8 cm

Diameter of paper roll without cylinder = 52 cm (60 - 8)

Length of paper = 104,000 cm (52/0.0005)

Length of paper in km = 1.04 km (104,000/100,000)

Thus, the length of the paper in kilometers will be 1.04 km.

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Answer 2

The area of the paper is the amount of space it occupies.

The length of papers around the edge is 1607680 cm

The given parameters are:

$\mathbf{d_1 = 60cm}$

$\mathbf{d_2 = 60cm + 8cm = 68cm}$

The area of the circle head is:

$\mathbf{Area = \pi \frac{d^2}{4}}$

So, we have:

$\mathbf{Area = \pi \frac{d_2^2 - d_1^2}{4}}$

Substitute known values

$\mathbf{Area = \pi \frac{68^2 - 60^2}{4}}$

$\mathbf{Area = \pi \frac{1024}{4}}$

$\mathbf{Area = 256\pi}$

The length of the paper is then calculated as:

$\mathbf{Length = \frac{Area}{0.0005}}$

This gives

$\mathbf{Length = \frac{256\pi}{0.0005}}$

$\mathbf{Length = \frac{256 \times 3.14}{0.0005}}$

$\mathbf{Length = 1607680}$

Hence, the length of papers around the edge is 1607680 cm

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