stereometria eheheh: Oblicz objętość stożka, którego pole podstawy jest równe 16, a pole powierzchni bocznej wynosi 20.

Janek191: Pp = 16 Pb = 20 zatem Pp = π r² = 16 ⋀ Pb = π r l = 20 czyli Pp / Pb = ( π r² ) / ( π r l ) = r/l = 16/20 = 4/5 4 l = 5 r l = ( 5/4) r −−−−−−−−−−−−−−− l² = (25/16) r² Z Tw. Pitagorasa mamy h² + r² = l² h² = l² − r² = (25/16) r² − r² = (9/16) r² h = (3/4) r −−−−−−−−−−−−− π r² = 16 => r² = 16/π => r = 4/√π więc h = (3/4) * ( 4/√π ) = 3/ √π Objętość stożka V = ( 1/3) Pp *h V = (1/3) *16* [ 3/ √π ] = 16/ √π ==============================