Ab x h
V=--------------=
3
h
sin α =------- ⇒ h= a sin α
a
d =diagonala bazei
(d /2)² = a²- h² = a² - a² sin²α = a²(1-sin²α)
d /2 = a√(1-sin²α)
d=2a(1-sin²α)
latura bazei = b
d² = 2b²
b²=d²/2 =[ 2a(1-sin²α)]²/2 = 4a²(1-sin²α)²/2=2a²(1-sin²α)²
b =a(1-sin²α)√2
Ab x h 2 a²(1-sin²α)² xa sin α 2a³ sinα(1-sinα²)
V=------------- = --------------------------------- = -------------------------
3 3 3
