• Author / Uploaded
• Nelson Antonio Mamani Ape

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FÓRMULAS DE LAS ÁREAS Y VOLÚMENES DE LOS CUERPOS GEOMÉTRICOS Cuerpos

Área total (AT)

Área lateral (AL)

Área base/s (AB)

PRISMAS RECTOS

AT = AL + 2AB

h

AL = PB · h

AB =

Volumen (V)

b · a (1) 2 l2 (2) P · ap (3) 2

V = AB · h

ORTOEDRO

AT = 2ab+2ac+2bc

c

AL = 2ac+2bc

AB = 2ab

V = a·b·c

AB = 2a2

V = a3

b a CUBO

AT = 6a2

a

AL = 4a2

PIRÁMIDES RECTAS ap

AT = AL + AB

h

AL =

PB ⋅ ap 2

AB =

b · a (1) 2 l2 (2) P · ap (3) 2

V=

1 A ⋅h 3 B

ó V=

AB ⋅h 3

TRONCO DE PIRÁMIDE

Bm

AT = AL+ABM+ABm BM

CILINDRO r h

( B + b) ⋅ a ⋅n 2

AB = igual que en la pirámide

AT = AL + 2AB AT = 2πrg + 2πr2

g

CONO

g

AL =

AL = 2πrg

AB = πr2

AT = AL + AB

h

r

AT = πrg + πr2

V = πr2 · h

V= AL = πrg

AB = πr2

1 ⋅π r 2 ⋅ h 3

ó V=

π r 2 ⋅h 3

TRONCO DE CONO

r

AT=πg(R+r)+πR2+πr2

g R

AL = πg·(R+r)

ABM = πR2 ABm = πr2

ESFERA r

A = 4πr

2

V=

(1) Base triangular (b=base, a=altura). (2) Base cuadrada (l=lado). (3) Polígono regular (P=perímetro, ap=apotema).

4 ⋅π r 3 3