Odpowiedzi

2010-04-07T16:12:00+02:00
R = 2√13
R - promień kuli
r - promień walca wpisanego w tę kulę
h - wysokość walca
Mamy
r/h = 3/4 ---> 4r = 3h --> 2r = (3/2) h
oraz h² + (2r)² =(2 R)² = 4 R²
h² + [( 3/2) h]² =4* [2√13]²
h² + (9/4) h² = 4*4*13 =16*13
(4/4) h² + (9/4) h² = 16*13
(13/4) h² = 16 * 13
h² = 16*13*(4/13) = 64
h = √64 = 8
2r = (3/2)*h = (3/2)* 8 = 12
r = 6
Pc = 2*Pp + Pb = 2*π*r² + 2*π *r * h =
= 2*π *6² + 2*π *6 *8 = 72 π + 96 π = 168 π
V = Pp*h = π r² *h = π *6² *8 = 288 π
Odp. Pc = 168 π oraz V = 288 π.