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Pc = 30π cm² - pole calkowite walca
r = 1/5h
h = 5*r
V = ?
1. Obliczam promień r podstawy
Pc = 30π cm²
Pc = 2*Pp + Pb
2*Pp + Pb = 30π cm²
2*π*r² + 2πr*h = 30 π cm²
2π( r² + r*h ) = 30π cm² /:2π
r² + r*h = 15
r² + r*5r = 15
r² + 5r² = 15
6r² -15 = 0
3(2r² -5 ) = 0 /:3
2r² -5 = 0
2r² = 5
r² = 5/2
r = √(5/2)
r = √5 : √2
r = (√5 :√2)*(√2 :√2)
r = √5*√2: 2
r = (1/2)*√10
2. Obliczam wysokość h
h = 5r
h = 5*(1/2)*√10 )
h = (5/2)*√10
3. Obliczam objetość walca
V = Pp *h
V = πr²*h
V = π*[(1/2)*√10]² *(5/2)*√10
V = π*(1/4)*10 *(5/2)*√10
V = π*(25/4)*√10
V = (25/4)π√10