$\frac{P_b}{P_p}=\frac{\sqrt{2}}{1}$  

$\frac{\pi rl}{\pi r^2}=\frac{\sqrt{2}}{1}$  

$\frac{l}{r}=\frac{\sqrt{2}}{1}$  

$l=\sqrt{2}r$  

 

$r^2+h^2=l^2$  

$r^2+h^2={\left(\sqrt{2}r\right)}^2$  

$h^2=2r^2-r^2$  

$h^2=r^2$  

$h=r$  

 

$V_{◯}=\frac{4}{3}\pi r^3=\frac{4}{3}\pi 3^3=\frac{4}{3}\pi \cdot 27=36\pi$  

$V_s=36\pi$  

$\frac{1}{3}\pi r^{2}h=36\pi \mid :\pi$  

$\frac{1}{3}{r}^{2}h=36\mid \cdot 3$  

$r^{2}h=108$  

$r^3=108$  

$r^3=3^3\cdot 4$  

$r=3\sqrt[3]{4}$  

 

$\frac{r}{l}=\cos \alpha$  

$\frac{r}{\sqrt{2}r}=\cos \alpha$  

$\frac{1}{\sqrt{2}}=\cos \alpha$  

$\frac{\sqrt{2}}{2}=\cos \alpha$  

$\cos {45}^o=\cos \alpha$  

$\alpha ={45}^o$