Question

Un cilindru circular drept are raza si generatoarea d.p cu 3 si 5. At=192Π(pi) cm. Calculati volumul

Answer 1

G/5=r/3⇒r=3G/5(1)    At=πr(r+G)⇒192π=πr(r+G) (2)
vom inlocui rel(1) in rel(2)⇒192π=π3G/5(3G/5+G)⇒
192=9G²/25+3G²/5(aducem la acelasi numitor)⇒
4800=9G²+15G²⇒24G²=4800⇒G²=200⇒G=√200=10√2cm
r=3G/5=3·10√2/5=6√2cm
deci avem:r=6√2cm si G=10√2cm
V=πr²H/3→va trebui sa aflam H
H²=G²-r²⇒H=√G²-r²=√200-72=√128⇒H=8√2cm
V=πr²H/3=π(6√2)²·8√2/3=π·72·8√2/3⇒V=192√2πcm³