a) Liczymy pole koła według wzoru $P=\pi r^2$

$P=\pi \cdot 7^2=49\pi$   

 

$P=p\cdot i{\left(\frac{3}{5}\right)}^2=\frac{9}{25}\pi$

$P=\pi {\left(0.4\right)}^2=0.16\pi$

$P=\pi \cdot {\left(1.2\right)}^2=1.44\pi$

$P=\pi \cdot {\left(\frac{1}{2}\pi \right)}^2=\frac{1}{4}{\pi }^3$

$P=\pi {\left(\sqrt{6}\right)}^2=6\pi$

$P=\pi {\left(5\sqrt{2}\right)}^2=50\pi$

b) Liczymy najpier promień koła $r=\frac{1}{2}d$ oraz wyznaczamy pole koła według wzory $P=\pi r^2$

$r=\frac{8}{2}=4$         $P=\pi \cdot 4^2=16\pi$

   $r=\frac{5}{2}$           $P=\pi \cdot {\left(\frac{5}{2}\right)}^2=\frac{25}{4}\pi$

  $r=\frac{\frac{2}{3}}{2}=\frac{1}{3}$         $P=\pi {\left(\frac{1}{3}\right)}^2=\frac{1}{9}\pi$

  $r=\frac{2\pi }{2}=\pi$           $P=\pi {\left(\pi \right)}^2={\pi }^3$

  $r=\frac{4\sqrt{3}}{2}=2\sqrt{3}$       $P=\pi {\left(2\sqrt{3}\right)}^2=12\pi$

  $r=\frac{\sqrt{5}}{2}$                 $P=\pi {\left(\frac{\sqrt{5}}{2}\right)}^2=\frac{5}{4}\pi$

    $r=\frac{\frac{2}{7}\sqrt{2}}{2}=\frac{1}{7}\sqrt{2}$ $P=\pi {\left(\frac{1}{7}\sqrt{2}\right)}^2=\frac{2}{49}\pi$

c) Mamy dane pole koła. $P=\pi r^2$

$r^2=\frac{P}{\pi }$

$r=\sqrt{\frac{P}{\pi }}$

$r=\sqrt{\frac{\pi }{\pi }}=\sqrt{1}=1$   

  $r=\sqrt{\frac{\frac{1}{16}\pi }{\pi }}=\sqrt{\frac{1}{16}}=\frac{1}{4}$   

  $r=\sqrt{\frac{1.21\pi }{\pi }}=\sqrt{1.21}=1.1$  

    $r=\sqrt{\frac{\frac{1}{5}\pi }{\pi }}=\sqrt{\frac{1}{5}}=\frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5}$   

   $r=\sqrt{\frac{4}{\pi }}$     

  $r=\sqrt{\frac{5}{\pi }}$   

   $r=\sqrt{\frac{\frac{9}{\pi }}{\pi }}=\sqrt{\frac{9}{{\pi }^2}}=\frac{3}{\pi }$    

d) Korzystamy z poprzedniego podpunku

$d=2r=2\sqrt{\frac{P}{\pi }}$

$d=2\sqrt{\frac{\frac{4}{25}\pi }{\pi }}=2\sqrt{\frac{4}{25}}=2\cdot \frac{2}{5}=\frac{4}{5}$

$d=2\sqrt{\frac{0.09\pi }{\pi }}=2\sqrt{0.09}=2\cdot 0.3=0.6$

$d=2\sqrt{\frac{7\pi }{\pi }}=2\sqrt{7}$

$d=2\sqrt{\frac{\frac{1}{3}\pi }{\pi }}=2\sqrt{\frac{1}{3}}$

$d=2\sqrt{\frac{81}{\pi }}=2\cdot \frac{9}{\sqrt{\pi }}=\frac{18}{\sqrt{\pi }}$

$d=2\sqrt{\frac{3}{\pi }}=\frac{2\sqrt{3}}{\sqrt{\pi }}$