Odpowiedzi

2010-03-21T23:53:05+01:00
A - długość boku kwadratu
b - długość boku trójkąta równobocznego
Mamy
4a = 3 b = 24 cm ---> a = 24 cm : 4 = 6 cm
oraz b = 24 cm : 3 = 8 cm
Walec
r = a :2 = 6 cm :2 = 3 cm
h = a = 6 cm
V = π r² h = π *( 3 cm)² * 6 cm = 54 π cm³
Pc = 2*Pp + Pb = 2* π r² + 2 π r h
Pc = 2 *π (3 cm)² + 2 π * 3 cm * 6 cm =
= 18 π cm² + 36 π cm² = 54 π cm²
Stożek
r = b : 2 = 8 cm :2 = 4 cm
h = (b√3)/2 = ( 8 √3)/2 cm = 4√3 cm
V = (1/3)*π r² h = (1/3)*π *(4 cm)² * 4√3 cm = (1/3)*64√3 cm³ =
= (64/3)*√3 cm³
Pc= Pp + Pb = π r² + π r l
l² = r² + h²
l² = 4² +(4√3)² = 16 + 16*3 = 64
l = √64 = 8
Pc = π *(4 cm)² + π *4 cm * 8 cm = 16 π cm² + 32 π cm² =
= 48 π cm².