The document contains formulas for calculating geometric properties of various 3D solids. It lists direct and inverse formulas for calculating the area, total area, volume, and dimensions of solids such as parallelepipeds, cubes, prisms, pyramids, cylinders, cones, spheres, and regular polyhedra. The formulas relate properties like base area, total area, volume, height, length of sides, radius, and circumferences.

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

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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