$\text{I.}\text{P}$  

$\text{II.}\text{P}$  

$\text{III.}P=\frac{\alpha }{{360}^o}\cdot \pi r^2$  

$108\pi {\text{cm}}^2=\frac{{270}^o}{{360}^o}\cdot \pi r^2\mid :\pi$  

$108{\text{cm}}^2=\frac{27}{36}\cdot r^2\mid :\frac{27}{36}$  

$108{\text{cm}}^2:\frac{27}{36}=r^2$  

$r^2={\sout{108}}^4{\text{cm}}^2\cdot \frac{36}{{\sout{27}}^1}=144{\text{cm}}^2$  

$r^2=144{\text{cm}}^2\mid \sqrt{}$  

$r=12\text{cm}$  

$12\text{cm}>10\text{cm}\text{P}$   

Zdanie jest prawdziwe.

$\text{IV.}6\pi \text{cm}=\frac{\alpha }{{360}^o}\cdot 2\pi \cdot 10\text{cm}$  

$6\pi \text{cm}=\frac{\alpha }{{360}^o}\cdot 20\pi \text{cm}\mid :\pi \text{cm}$  

$6=\frac{\alpha }{{360}^o}\cdot 20\mid \cdot {360}^o$  

${2160}^o=\alpha \cdot {20}^o\mid :{20}^o$  

$\alpha ={108}^o\text{F}$   

Zdanie jest fałszywe. Kąt o mierze 108° nie jest kątem ostrym.