$20 \cdot 103$ Wrap a $5 \mathrm{~cm}$ wide strip of paper around a cardboard cylinder with a diameter of $2 \mathrm{~cm}$, 600 times to form a cylinder with a diameter of $10 \mathrm{~cm}$ (assuming the paper strip is wound into 600 concentric cylinders, whose diameters uniformly change from $2 \mathrm{~cm}$ to $10 \mathrm{~cm}$. In meters $(\mathrm{m})$, the length of the paper strip is 
(A) $36 \pi$.
(B) $45 \pi$.
(C) $60 \pi$.
(D) $72 \pi$.
(E) $90 \pi$.
(38th American High School Mathematics Examination, 1987)
［Solution］Since the paper strip is wound uniformly, its radius changes in an arithmetic sequence (common difference being the thickness of the paper $d$). Because the paper is very thin, each loop can be approximately regarded as a circle (strictly speaking, this is not the case).

The circumference of a circle is $2 \pi r$ or $\pi D$, so the length of each loop of paper will also change with a common difference of $2 \pi d$. Therefore, the average length can be taken as the middle value, so

Length of the paper strip $=600 \cdot \pi \cdot 6=3600 \pi(\mathrm{cm})=$ $36 \pi(\mathrm{m})$.
Therefore, the answer is $(A)$.