Stim ca Aria laterala are formula:
Al=Pi*R*G=544 Pi , deci:
G=[tex] \frac{544}{R} [/tex]
Cu Teorema lui Pitagora:
[tex] G^{2} = R^{2} + H^{2} [/tex] deci
[tex] G^{2} = R^{2} + 30^{2} [/tex] si inlocuim G din prima formula:
[tex] ( \frac{544}{R} )^{2} = R^{2} + 30^{2} [/tex]
[tex] 544^{2} = R^{4} + 30^{2} * R^{2} [/tex]
Completam pana la un patrat perfect in membrul drept si obtinem:
[tex] ( R^{2} +450)^{2} - 706^{2} [/tex]=0
[tex]( R^{2} +450+706)( R^{2} +450-706)[/tex]=0
[tex]( R^{2} +1156)( R^{2} -256)[/tex]=0
deci [tex] R^{2} -256[/tex]=0 are solutii numere reale, adica:
[tex] R^{2} - 16^{2} [/tex]=0
(R-16)(R+16)=0
R=16 cm
G=[tex] \frac{544}{16} [/tex]=34 cm
