3-3. The height of a truncated cone is equal to the radius of its larger base; the perimeter of a regular hexagon circumscribed around the smaller base is equal to the perimeter of an equilateral triangle inscribed in the larger base. Determine the angle of inclination of the cone's generatrix to the base plane.
Solution 3. Let $R$ be the radius of the larger base circle, and $r$ be the radius of the smaller base circle. The perimeter of the regular hexagon circumscribed around the smaller base is $\frac{12 r}{\sqrt{3}}$. The perimeter of the regular hexagon inscribed in the larger base is $3 R \sqrt{3}$. According to the condition, $\frac{12 r}{\sqrt{3}}=3 R \sqrt{3}$, i.e., $r=\frac{3}{4} R$. If $\varphi$ is the desired angle of inclination, then $\operatorname{tg} \varphi=\frac{R}{R-r}=4$.

## 4th Option