Formulario solidi
description
Transcript of Formulario solidi
Tav
ole
13
FORMULARIO DI GEOMETRIA SOLIDA
Solido Formule dirette Formule inverse
Parallelepipedo rettangolo
d
b
c
a
A l � pb h oppure
A l � 2(ab � bc)
A t � A l � 2A b oppure
A t � 2(ab � ac � bc)
V � abc oppure V � A bh
d � �a2 � b�2 � c2�
p b � �A
hl
� h � �A
pb
l�
A l � A t � 2A b A b � �A t �
2
A l�
A b � �V
h� h � �
A
V
b
�
Cubo
ds
Come il parallelepipedo, oppure:
A l � 4 s2 A t � 6 s2
V � s3
d � s �3� � s � 1,73
s � ��A
4l
�� s � ��A
6t
��s �
3� V�
Prisma retto
A l � pb h
A t � A l � 2A b
V � A b h
pb � �A
hl
� h � �A
pb
l�
A l � A t � 2A b A b � �A t �
2
A l�
A b � �V
h� h � �
A
V
b
�
Piramide retta
l
ha
A l � �p
2b a� A t � A l � A b
V � �A
3b h�
pb � �2
a
A l� a � �
2
p
A
b
l�
A b � �3
h
V� h � �
3
A
V
b
�
Tav
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14
Solido Formule dirette Formule inverse
Cilindro
r
h A l � 2prh A t � A l � 2A b
V � pr2 h
r � �2p
A
h� h � �
2
A
p r�
A l � A t � 2A b A b � �A t �
2
A l�
h � �p
V
r2� r � ��
p
V
h��
Cono
C: misura della circonferenza di base
h
a
r
A l ��C
2
�a� �pra
A l � pra
A t � A l � Ab � pra � pr2
V � �pr
3
2 h�
a � �p
A
rl
� r � �p
A
al
�
r � ��3
p
V
h�� h � �
p
3V
r2�
Sfera
r
A � 4pr 2 V � �4
3� pr3
r � ��4
A
p
�� r �
3
��4
3V
p
��
Poliedri regolari Area totale Volume
Tetraedro 4 � l2 �0,433 l3 �0,117
Esaedro o Cubo 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