A right circular cone has a slant height of $27 \mathrm{~cm}$; if we unroll the lateral surface, the resulting sector has an angle of $220^{\circ}$. What is the radius of the base of the cone?
Let's denote the radius of the base of the cone by \( r \). According to the condition,

\[
2 r \pi = \frac{2 \pi}{360} 220 \cdot 27
\]

from which

\[
r = 16.5 \text{ cm}
\]

(Sebestyén István, Budapest, high school student.)

Number of solutions: 27.