This document provides formulas for calculating the total area, lateral area, base area, and volume of various geometric solids. It lists the following shapes: prisms, orthoprisms, cubes, pyramids, truncated pyramids, cylinders, cones, truncated cones, and spheres. For each shape, it gives the relevant formulas to calculate their total area, lateral area, base area(s), and volume.

1. FÓRMULAS DE LAS ÁREAS Y VOLÚMENES DE LOS CUERPOS GEOMÉTRICOS
Cuerpos Área total (AT) Área lateral (AL) Área base/s (AB) Volumen (V)
PRISMAS RECTOS b · a (1)
2
AT = AL + 2AB AL = PB · h AB = l2 (2) V = AB · h
h P · ap (3)
2
ORTOEDRO
c AT = 2ab+2ac+2bc AL = 2ac+2bc AB = 2ab V = a·b·c
b
a
CUBO
AT = 6a2 AL = 4a2 AB = 2a2 V = a3
a
PIRÁMIDES
RECTAS b · a (1) 1
2 V= A ⋅h
3 B
ap AT = AL + AB PB ⋅ ap AB = l2 (2) ó
h AL =
2 P · ap (3) AB ⋅h
2 V=
3
TRONCO DE
PIRÁMIDE
Bm ( B + b) ⋅ a
AT = AL+ABM+ABm AL = ⋅n AB = igual que en la
BM 2
pirámide
CILINDRO AT = AL + 2AB
r
AT = 2πrg + 2πr2 AL = 2πrg AB = πr2 V = πr2 · h
h g
CONO AT = AL + AB 1
V= ⋅π r 2 ⋅ h
3
AT = πrg + πr2 AL = πrg AB = πr2 ó
g h r
π r 2 ⋅h
V=
3
TRONCO DE CONO
r
g AT=πg(R+r)+πR2+πr2 AL = πg·(R+r) ABM = πR2
R ABm = πr2
ESFERA
4
r V= ⋅π r 3
A = 4πr 2
3
(1) Base triangular (b=base, a=altura). (2) Base cuadrada (l=lado). (3) Polígono regular (P=perímetro, ap=apotema).