On a $2 \times 30$ minute cassette tape, the smallest diameter of the tape reel is $2 \mathrm{~cm}$, and the largest diameter is $4.5 \mathrm{~cm}$. What is the thickness of the tape? (The playback speed is $4.75 \mathrm{~cm} / \mathrm{s}$. )
The length of the belt is $l=4.75 \mathrm{~cm} / \mathrm{s} \cdot 1800 \mathrm{~s}=8550 \mathrm{~cm}$. We will calculate the volume of the belt in two ways.

1993-02-092-1.eps

$1993-02-092-2 . e p s$

On one hand, $V=l \cdot x \cdot y$, where $x$ is the sought thickness, and $y$ is the width of the belt. On the other hand, in its rolled-up state, $V=y\left(R^{2}-r^{2}\right) \pi$, where $R$ is the largest, and $r$ is the smallest radius. From these two expressions,

$$
x=\frac{\left(R^{2}-r^{2}\right) \pi}{l}=0.015 \mathrm{~mm}
$$