Formula di Geometria Solida

1. Ta
v
ol
e
FORMULARIO DI GEOMETRIA SOLIDA
Solido Formule dirette Formule inverse
Parallelepipedo rettangolo
A l ϭ pb h oppure
A l ϭ 2(ab ϩ bc) Al Al
p b ϭ ᎏᎏ h ϭ ᎏᎏ
h pb
c
d A t ϭ Al ϩ 2Ab oppure At Ϫ Al
A l ϭ A t Ϫ 2A b A b ϭ ᎏᎏ
A t ϭ 2(ab ϩ ac ϩ bc) 2
b
a V V
V ϭ abc oppure V ϭ A b h A b ϭ ᎏᎏ h ϭ ᎏᎏ
h Ab
d ϭ ͙a 2 ϩ b2 ϩ c 2
ෆෆ
Cubo
Come il parallelepipedo, oppure:
͙ᎏ4ᎏ
๶ ͙ᎏ6ᎏ
๶
s
A l ϭ 4 s2 A t ϭ 6 s2 Al At
d sϭ sϭ
V ϭ s3
s ϭ ͙ෆ
3
V
d ϭ s ͙3 Ϸ s и 1,73
ෆ
Prisma retto
Al Al
p b ϭ ᎏᎏ h ϭ ᎏᎏ
A l ϭ pb h h pb
At Ϫ Al
A t ϭ Al ϩ 2Ab Al ϭ At Ϫ 2Ab A b ϭ ᎏᎏ
2
V ϭ Abh V V
A b ϭ ᎏᎏ h ϭ ᎏᎏ
h Ab
Piramide retta
pb a 2Al 2Al
A l ϭ ᎏᎏ A t ϭ Al ϩ Ab pb ϭ ᎏᎏ a ϭ ᎏᎏ
2 a pb
h
a A h 3V 3V
V ϭ ᎏbᎏ A b ϭ ᎏᎏ h ϭ ᎏᎏ
3 h Ab
l
13

2. e
ol
v
Ta
Solido Formule dirette Formule inverse
Cilindro
r A A
r ϭ ᎏᎏ h ϭ ᎏᎏ
2p h 2p r
h A l ϭ 2pr h A t ϭ Al ϩ 2Ab At Ϫ Al
A l ϭ A t Ϫ 2A b A b ϭ ᎏᎏ
V ϭ pr h
2 2
͙ ᎏᎏ
๶
V V
h ϭ ᎏᎏ rϭ
pr2 ph
Cono
C иa
A l ϭ ᎏᎏ ϭ pr a
a
2 Al Al
A l ϭ pr a a ϭ ᎏᎏ r ϭ ᎏᎏ
h pr pa
A t ϭ A l ϩ A b ϭ pr a ϩ pr 2
͙ᎏᎏ
๶
r 3V 3V
rϭ h ϭ ᎏᎏ
C: misura della circonferenza di base ph pr2
pr 2 h
V ϭ ᎏᎏ
3
Sfera
r
4
͙๶ ͙ᎏᎏ
๶
A ϭ 4pr 2 V ϭ ᎏᎏ pr 3 A 3 3V
3 rϭ ᎏᎏ rϭ
4p 4p
Poliedri regolari Area totale Volume
Tetraedro 4 и l и 0,433
2 l и 0,117
3
Esaedro o Cubo 6 и l2 l3 и 1
Ottaedro 8 и l2 и 0,433 l3 и 0,471
Dodecaedro 12 и l2 и 1,720 l3 и 7,663
Icosaedro 20 и l2 и 0,433 l3 и 2,182
14