Geometria-

Formule utilizzate:

raggio $\small r= \sqrt{\dfrac{A·360°}{\pi·\alpha}};$

raggio $\small r= \dfrac{2·A_s}{l};$

raggio $\small r= \dfrac{180°·l}{\pi·\alpha};$

circonferenza $\small c= r·2\pi;$

arco $\small l= \dfrac{r·\pi·\alpha}{180°};$

angolo del settore $\small \alpha= \dfrac{180°·\pi}{r·\pi};$

area del cerchio $\small A= r^2·\pi;$

area del settore $\small A_s= \dfrac{l·r}{2}.$

ti ho compilato solo il N°1 ; di seguito trovi tutti i valori calcolati per completare la tabella 

1

As = 20π = π*r^2*α/360°

r = √20*360/18 = √400 = 20 cm

C = 2πr = 40π cm

l = C*α/360 = 40π/20 = 2π cm

A = πr^2 = 400π cm^2

2

A = 1600π cm^2 = πr^2

r = √1600 = 40 cm

As = A*α/360° = 1600π*225°/360° = 1000π cm^2

C = 2πr = 80π cm

l = C*α/360° = 80π*225°/360° = 50π cm

3

A = 324π cm^2 = πr^2

r = √324 = 18 cm

As = 108π = π*r^2*α/360°

α = 360°*As/A = 360*108/324 = 120°

C = 2πr = 36π cm

l = C*α/360 = 36π/3 = 12π cm

4

A = 576π cm^2 = πr^2

r = √576 = 24 cm

As = 72π = π*r^2*α/360°

α = 360°*As/A = 360°*72/576 = 45°

C = 2πr = 48π cm

l = C*α/360 = 48π*45°/360° = 6π cm

5

C = 2πr = 30π cm

r = 30/2= 15 cm

l = 9π cm

α = 360°*l/C = 360*9/30 = 108°

A = πr^2 = 225π cm^2

As = A*α/360° = 225π*108°/360° = 67,5π cm^2

6

A = 441π cm^2 = πr^2

r = √441 = 21 cm

As = A*α/360° = 441π*72°/360° = 88,20π cm^2

C = 2πr = 42π cm

l = C*α/360 = 42π/5 = 8,4π cm