Ta v ol e 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 Ab ⫽ ᎏ ᎏ 2 A l ⫽ A t ⫺ 2A b V A b ⫽ ᎏᎏ h V h ⫽ ᎏᎏ Ab d ⫽ 兹苶 a 2 ⫹ b2苶 ⫹ c2 Cubo Come il parallelepipedo, oppure: s d A l ⫽ 4 s2 A t ⫽ 6 s2 V ⫽ s3 s⫽ ᎏ 兹ᎏ莦 4 Al s⫽ ᎏ 兹ᎏ莦 6 At s ⫽ 兹苶 V 3 d ⫽ s 兹3 苶 ⬇ 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 Ab ⫽ ᎏ ᎏ 2 V h ⫽ ᎏᎏ Ab Piramide retta p a A l ⫽ ᎏbᎏ 2 A t ⫽ Al ⫹ Ab 2A pb ⫽ ᎏᎏl a 2A a ⫽ ᎏᎏl pb 3V A b ⫽ ᎏᎏ h 3V h ⫽ ᎏᎏ Ab h a l A h V ⫽ ᎏbᎏ 3 13 Ta v e ol Solido Formule dirette Formule inverse Cilindro r A r ⫽ ᎏᎏ 2p h h A l ⫽ 2pr h A t ⫽ Al ⫹ 2Ab A h ⫽ ᎏᎏ 2p r At ⫺ Al Ab ⫽ ᎏ ᎏ 2 A l ⫽ A t ⫺ 2A b V ⫽ pr h 2 V h ⫽ ᎏᎏ pr2 r⫽ ᎏ 兹ᎏ莦 ph V Cono a h C ⭈a A l ⫽ ᎏᎏ ⫽ pr a 2 A l ⫽ pr a A a ⫽ ᎏᎏl 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 3V h ⫽ ᎏᎏ pr2 r⫽ 兹莦 r⫽ pr 2 h V ⫽ ᎏᎏ 3 3V Sfera r 4 V ⫽ ᎏᎏ pr 3 3 A ⫽ 4pr 2 Poliedri regolari Tetraedro Area totale Volume l ⭈ 0,117 6 ⭈ l2 l3 ⭈ 1 Ottaedro 8 ⭈ l2 ⭈ 0,433 l3 ⭈ 0,471 Dodecaedro 12 ⭈ l2 ⭈ 1,720 l3 ⭈ 7,663 Icosaedro 20 ⭈ l2 ⭈ 0,433 l3 ⭈ 2,182 2 ᎏ 兹ᎏ莦 4p 3 4 ⭈ l ⭈ 0,433 Esaedro o Cubo 14 A ᎏᎏ 4p 3 3V