[ [ Cross-sectional area $]$

The lateral edge of the pyramid is divided into 100 equal parts, and planes parallel to the base are drawn through the points of division. Find the ratio of the areas of the largest and smallest of the resulting cross-sections.

#
Let $S$ be the area of the base of the pyramid, $S_1$ and $S_2$ be the areas of the largest and smallest sections, respectively. The largest and smallest sections are polygons similar to the polygon of the base of the pyramid with coefficients $\frac{99}{100}$ and $\frac{1}{100}$, respectively. Therefore,

$$
S_1 = \left(\frac{99}{100}\right)^2 \cdot S, \quad S_2 = \left(\frac{1}{100}\right)^2 \cdot S.
$$

Thus,

$$
\frac{S_1}{S_2} = \frac{\left(\frac{99}{100}\right)^2 \cdot S}{\left(\frac{1}{100}\right)^2 \cdot S} = 9801
$$

## Answer

9801.