Oznaczenia:

P - pole koła

L - obwód koła

r - promień koła

d - średnica koła

 

$a)P_1=\pi \cdot {\left(1cm\right)}^2=\pi c{m}^2$  

$P_2=\pi \cdot {\left(0,3km\right)}^2=0,09\pi k{m}^2$  

$P_3=\pi \cdot {\left(\frac{2}{3}mm\right)}^2=\frac{4}{9}\pi m{m}^2$  

$P_4=\pi \cdot {\left(2dm\right)}^2=4\pi d{m}^2$  

 

$L_1=2\pi \cdot 1cm=2\pi cm$  

$L_2=2\pi \cdot 0,3km=0,6\pi km$ $L_2=2\pi \cdot 0,3km=0,6\pi km$  

$L_3=2\pi \cdot \frac{2}{3}mm=\frac{4}{3}\pi mm$  

$L_4=2\pi \cdot 2dm=4\pi dm$  

 

 

 

$b)r_1=1km:2=0,5km$  
$r_2=2,4m:2=1,2m$  

$r_3=\frac{2}{7}cm:2=\frac{1}{7}cm$  

$r_4=7dm:2=3,5dm$  

 

$P_1=\pi \cdot {\left(0,5km\right)}^2=0,25\pi k{m}^2$  

$P_2=\pi \cdot {\left(1,2m\right)}^2=1,44\pi m^2$  

$P_3=\pi \cdot {\left(\frac{1}{7}cm\right)}^2=\frac{1}{49}\pi c{m}^2=\frac{\pi }{49}c{m}^2$  

$P_4=\pi \cdot {\left(3,5dm\right)}^2=12,25\pi d{m}^2$        $\left(3,5\cdot 3,5=3\frac{1}{2}\cdot 3\frac{1}{2}=\frac{7}{2}\cdot \frac{7}{2}=\frac{49}{4}=12\frac{1}{4}=12,25\right)$  

$L_1=\pi \cdot 1km=\pi km$  

$L_2=\pi \cdot 2,4m=2,4\pi m$  

$L_3=\pi \cdot \frac{2}{7}cm=\frac{2}{7}\pi cm$  

$L_4=\pi \cdot 7dm=7\pi dm$  

 

 

 

$c)2\pi r_1=6dm\Rightarrow r_1=\frac{6}{2\pi }dm=\frac{3}{\pi }dm$  

$2\pi r_2=3,2mm\Rightarrow r_2=\frac{3,2}{2\pi }mm=\frac{1,6}{\pi }mm$  
$2\pi r_3=\pi km\Rightarrow r_3=\frac{\pi }{2\pi }km=\frac{1}{2}km$  

$2\pi r_4=4\pi cm\Rightarrow r_4=\frac{4\pi }{2\pi }cm=2cm$  

$d)\pi r_1^2=1c{m}^2\Rightarrow r_1^2=\frac{1}{\pi }c{m}^2\Rightarrow r_1=\sqrt{\frac{1}{\pi }}cm=\frac{1}{\sqrt{\pi }}cm=\frac{\sqrt{\pi }}{\pi }cm\Rightarrow d_1=2\cdot \frac{\sqrt{\pi }}{\pi }cm=\frac{2\sqrt{\pi }}{\pi }cm$  
$\pi r_2^2=3ha=300m^2\Rightarrow r_2^2=\frac{300}{\pi }{m}^2\Rightarrow r_2=\sqrt{\frac{300}{\pi }}m=\frac{\sqrt{300}}{\sqrt{\pi }}m=\frac{10\sqrt{3}}{\sqrt{\pi }}m=\frac{10\sqrt{3\pi }}{\pi }m\Rightarrow d_2=\frac{20\sqrt{3\pi }}{\pi }m$  

$\pi r_3^2=\pi d{m}^2\Rightarrow r_3^2=1d{m}^2\Rightarrow r_3=\sqrt{1}dm=1dm\Rightarrow d_3=2dm$  

$\pi r_4^2=\frac{\pi }{2}m{m}^2\Rightarrow r_4^2=\frac{1}{2}m{m}^2\Rightarrow r_4=\sqrt{\frac{1}{2}}mm=\frac{1}{\sqrt{2}}mm=\frac{\sqrt{2}}{2}mm\Rightarrow d_4=2\cdot \frac{\sqrt{2}}{2}mm=\sqrt{2}mm$