Formulario geometria solida PDF

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Description

Ta v

o le

FORMULARIO DI GEOMETRIA SOLIDA Solido

Formule dirette

Parallelepipedo rettangolo

A l ⫽ pb h

oppure A p b ⫽ ᎏᎏl h

A l ⫽ 2(ab ⫹ bc) c

d b

Formule inverse

A t ⫽ Al ⫹ 2Ab

A h ⫽ ᎏᎏl pb

oppure

A t ⫽ 2(ab ⫹ ac ⫹ bc)

a

V ⫽ abc oppure V ⫽ A b h

At ⫺ Al ᎏ Ab ⫽ ᎏ 2

A l ⫽ A t ⫺ 2A b V A b ⫽ ᎏᎏ h

V h ⫽ ᎏᎏ Ab

⫹ c2 a 2 ⫹ b2苶 d ⫽ 兹苶 Cubo Come il parallelepipedo, oppure: s d

A l ⫽ 4 s2

A t ⫽ 6 s2

V ⫽ s3

s⫽

兹ᎏ莦4ᎏ Al

s⫽

ᎏ 兹ᎏ莦 6 At

V s ⫽兹 苶 3

d ⫽ s 兹苶 3 ⬇ s ⭈ 1,73

Prisma retto

A l ⫽ pb h

A p b ⫽ ᎏᎏl h

A h ⫽ ᎏᎏl pb

A t ⫽ Al ⫹ 2Ab

Al ⫽ At ⫺ 2Ab

V ⫽ Abh

V A b ⫽ ᎏᎏ h

At ⫺ Al ᎏ A b ⫽ᎏ 2

V h ⫽ ᎏᎏ Ab

Piramide retta pa A l ⫽ ᎏb ᎏ 2 h

a l

A h V ⫽ ᎏb ᎏ 3

A t ⫽ Al ⫹ Ab

2A pb ⫽ ᎏᎏl a

2 Al a ⫽ ᎏᎏ pb

3V A b ⫽ ᎏᎏ h

3V h ⫽ ᎏᎏ Ab

13

Ta v

e ol Solido

Formule dirette

Formule inverse

Cilindro A r ⫽ ᎏᎏ 2p h

r h

A l ⫽ 2pr h

A t ⫽ Al ⫹ 2Ab

A h ⫽ ᎏᎏ 2p r At ⫺ Al ᎏ Ab ⫽ ᎏ 2

A l ⫽ A t ⫺ 2A b

2

V ⫽ pr h V h ⫽ ᎏᎏ pr2

r⫽

ᎏ 兹ᎏ莦 ph V

Cono a h

C ⭈a A l ⫽ᎏ ᎏ ⫽ pr a 2 A l ⫽ pr a

Al a ⫽ ᎏᎏ pr

A t ⫽ A l ⫹ A b ⫽ pr a ⫹ pr 2

r

C: misura della circonferenza di base

Al r ⫽ ᎏᎏ pa

r⫽

ᎏ 兹ᎏ莦 ph

r⫽

兹莦

pr 2 h V ⫽ ᎏᎏ 3

3V h ⫽ ᎏᎏ pr2

3V

Sfera

r

4 V ⫽ ᎏ ᎏ pr 3 3

A ⫽ 4 pr 2

Poliedri regolari Tetraedro

Area totale 2

Volume 3

l ⭈ 0,117

6 ⭈ l2

l3 ⭈ 1

8 ⭈ l2 ⭈ 0,433

l3 ⭈ 0,471

Dodecaedro

12 ⭈ l2 ⭈ 1,720

l3 ⭈ 7,663

Icosaedro

20 ⭈ l2 ⭈ 0,433

l3 ⭈ 2,182

Ottaedro

ᎏ 兹ᎏ莦 4p 3

r⫽

4 ⭈ l ⭈ 0,433

Esaedro o Cubo

14

A ᎏᎏ 4p

3V...