Rysunek pomocniczy w załączniku.
Z Tw.Pitagorasa obliczę promień walca:
h = 2 × x ∧ h = 2x ∧ h = 6 cm ⇒ x = 3 cm
[tex]x^{2} +r^{2} =R^{2} ~~\land~~x=3cm~~\land~~R=5cm\\\\r^{2} +(3cm)^{2} =(5cm)^{2}\\ \\r^{2} =25~cm^{2}-9~cm^{2} \\\\r^{2} =16~cm^{2} ~~\land~~r > 0~~\Rightarrow~~r=4~cm[/tex]
Obliczam objętość walca:
[tex]V=\pi \cdot r^{2} \cdot h~~\land~~r=4~cm~~\land~~h=6~cm\\\\V=\pi \cdot (4~cm) ^{2} \cdot 6~cm\\\\V=96\pi ~cm^{3}[/tex]
Odp: Objętość walca wynosi 96π cm³.
