Question

Na kuli o objętości 2304 pi cm3 opisano walec oblicz pole powierzchni całkowitej i objętość walca

Answer 1

V = 2304π cm³
V = 4/3 * π * r³
2304π cm³ = 4/3 * π * r³
2304 cm³ = 4/3 r³
576 cm³ = 1/3 r³
1728 cm³ = r³
r = ∛1728cm³ =

r = ∛8 * ∛216 cm =

r = ∛8 * ∛8 * ∛27 cm =

r = 2 * 2 * 3 cm = 12 cm

Pp = πr²
Pp = π12² = 144π cm²

l = 2πr
l = 2π12 = 24πcm

Pb = H * l
Pb = 24 cm * 24πcm =

Pb = 576π cm²

Pc = 2Pp + Pb
Pc = 2 * 144π + 576π =

Pc = 288π + 576π = 864πcm²

V = Pp * H
V = 144π cm² * 24cm =

V = 3456π cm³

Pozdrawiam! :D