efisiensi sc, bcc, dan fcc

1. Efisiensi kubus sederhana
V kubus = a^3
A = 2r, maka V kubus = 8r^3
V bola = 1 . 4/3πr^3 = 4/3πr^3
V ruang = 8r^3 - 4/3πr^3
= (8 - 4/3π ) r^3
= ((168-88)/21) r^3
= 80/21 r^3
Efisiensi Volume ruang = (80r^3)/21 . 21/(168r^3 ) . 100%
= 48%
Efisiansi kubus sederhana = 100% - 48% = 52%
2. efisiensi kubus pusat badan (bcc)
4r = a√3
a = 4r/√3 = 4/3r√3
Jika sisi kubus = a, maka V kubus = a^3
= 〖( 4/3 r√3)〗^3
= 64/27 3 √3 r^3
= 12,08r^3
bcc terdapat 2 bola maka V boloa = 2 . 4/3πr^3
= 8/3πr^3
= 8,37r^3
Efisiensi bcc = (8,37r^3)/(12,08r^3 ) . 100%
= 69%
3. efisiensi kubus pusat muka (fcc)
4r = a√2
a = 4r/√2 = 4/2r√2 = 2 r√2
Jika sisi kubus = a, maka V kubus = a^3
= 〖(2 r√2)〗^3
= 16√2 r^3
= 22,4r^3
fcc terdapat 4 bola maka V boloa = 4 . 4/3πr^3
= 16/3πr^3
= 16,7r^3
Efisiensi bcc = ( 16,7r^3)/(22,4r^3 ) . 100%
= 74%