Volumenes de Solidos

Cubo

Volumen:
$$a^{3}$$
Area:
$$6a^{2}$$
Diagonal:
$$\sqrt[2]{3}a$$
cubo

Prisma Rectangular(Recto) Paralelepipedo

Volumen:
$$a.b.c$$
Area:
$$2(ab+ac+bc)$$
Diagonal:
$$\sqrt[2]{a^2+b^2+c^2}$$
prisma rectangular

Prisma Oblicuo

Volumen:
$$A1.h$$
(principio de Cavalieri)
prisma oblicuo

Piramide Rectangular Recta

Volumen:
$$A1.h/3$$
piramide rectangular recta

Piramide Truncada

Volumen:
$$ \frac{h}{3}(A1+A2+\sqrt[2]{A1.A2})$$
Volumen:
$$ \cong h \frac{(A1+A2)}{2}$$
piramide truncada

Cilindro Circular Recto

Volumen:
$$\frac{\pi}{4} (d^2h)$$
Area lateral:
$$2\pi rh $$
Area Total:
$$2\pi r(r+h) $$
cilindro circular recto

Cilindro Hueco

Volumen:
$$ \frac{\pi}{4}h(D^2-d^2)$$
cilindro hueco

Cono Circular Recto

Volumen:
$$\frac{\pi}{3}r^2h $$
Area Lateral:
$$\pi rg$$
Area Total:
$$ \pi r(r+g) $$
cono circular recto

Cono Truncado

Volumen:
$$ \frac{\pi h}{3}(D^2+Dd+d^2) $$
Area Lateral:
$$ \pi(D+d)g $$
g:
$$ \sqrt[2]{ \frac{D-d}{2}^2+h^2} $$
cono truncado

Esfera

Volumen:
$$ \frac{4}{3} \pi r^3=\frac{1}{6} \pi d^3 $$
Area:
$$ 4 \pi r^2 = \pi d^2 $$
esfera

Segmento Esferico Truncado

Volumen:
$$ \frac{\pi}{6}h(3a^2 + 3b^2 + h^2 )$$
Area esferica:
$$ 2 \pi rh $$
Area Total:
$$ \pi(2rh+a^2+b^2) $$
segmento esferico truncado

Segmento Esferico

Volumen:
$$ \frac{\pi}{6}h(\frac{3}{4}s^2+h^2)=\pi h^2(r-\frac{h}{3})$$
Area esferica:
$$ 2 \pi rh= \frac{\pi}{4}(s^2+4h^2)$$
segmento esferico

Sector Esferico

Volumen:
$$ \frac{2}{3} \pi r^2h $$
Area total:
$$ \frac{\pi}{2} r(4h+s) $$
sector esferico

Esfera con perforacion cilindrica

Volumen:
$$ \frac{\pi}{6} h^3$$
Area total:
$$ 2 \pi h(R+r) $$
esfera perforacion cilindrica

Esfera con perforaciones conicas

Volumen:
$$ \frac{2}{3} \pi r^2h $$
Area total:
$$ 2 \pi r(h+ \sqrt[2]{r^2-h^2/4}) $$
esfera perforaciones conicas

Anillo de seccion circular

Volumen:
$$ \frac{\pi^2}{4} Dd^2 $$
Area:
$$ \pi^2 Dd $$
anillo seccion circular

Cilindro con corte inclinado

Volumen:
$$ \frac{\pi}{4} d^2h $$
cilindro corte inclinado

Cuña Cilindrica

Volumen:
$$ \frac{2}{3} r^2h $$
Area Lateral:
$$ 2rh $$
Area Total:
$$ 2rh + \frac{\pi}{2} r^2 + \frac{\pi}{2} r \sqrt[2]{r^2+h^2} $$
cuna cilindrica

Barril - Tonel

Volumen:
$$ \cong \frac{\pi}{12} h(2D^2+d^2) $$
barril

Prismatoide

Volumen:
$$ \frac{h}{6} (A1+A2+4A) $$
prismatoide