Es una magnitud métrica de tipo escalar definida como la extensión en tres dimensiones de una región del espacio. Es una magnitud derivada de la longitud, ya que se halla multiplicando la longitud, el ancho y la altura.[br][url=https://commons.wikimedia.org/wiki/File:Basic_shapes.svg][img width=220,height=159]https://upload.wikimedia.org/wikipedia/commons/thumb/3/38/Basic_shapes.svg/220px-Basic_shapes.svg.png[/img][/url][justify][url=https://commons.wikimedia.org/wiki/File:Basic_shapes.svg][/url][i]Cuerpos geométricas o figuras geométricas (solidos) que delimitan volúmenes.[br][/i][/justify]

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[color=#000000][color=#000000][color=#000000]En el área de geometría, sólido indica a una figura u objeto que consta de 3 dimensiones: ancho, largo y profundidad, por ende, ocupa un lugar en el espacio y posee volumen, por ejemplo: la pirámide y el cono.[br][br][/color][/color][/color][img 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[/img]

[color=#000000][color=#000000][color=#000000]Un [b]sólido de revolución[/b] es un cuerpo que puede obtenerse mediante una operación geométrica de rotación de una superficie plana alrededor de una recta que es contenida en su mismo plano. En principio, cualquier cuerpo con simetría axial o geométrica, es un sólido de revolució.[br][br][br][br]CARACTERISTICAS Y ELEMENTOS DE LOS SOLIDOS DE REVOLUCION 1. Tiene superficies curvas.[br] 2. Tiene infinitos planos de simetría que contienen al eje.[br] 3. No tiene aristas y por lo tanto, sus superficies no son polígonos.[url=https://1.bp.blogspot.com/-Coum-B4IF-4/UDbBsuf7VGI/AAAAAAAAABU/e2S9xDfr1_k/s1600/clip_image002_0003.jpg][img]https://1.bp.blogspot.com/-Coum-B4IF-4/UDbBsuf7VGI/AAAAAAAAABU/e2S9xDfr1_k/s1600/clip_image002_0003.jpg[/img][/url][br][br][br][br][br][br][br][br][br]4. Son generados por una figura plana que gira (Figura generatriz) sobre un lado recto que hace de eje de simetría. [br]5. Si la figura que lo genera (Figura generatriz) tiene un segmento perpendicular al eje, genera una cara circular. [br]6. Si la figura que lo genera  (Figura generatriz) tiene un segmento diagonal al eje, genera una zona cónica.[br] 7. Si la figura que lo genera  (Figura generatriz) tiene un segmento paralelo al eje, genera una zona cilíndrica. [br]8. Si la figura que lo genera (Figura generatriz) tiene media circunferencia, genera una zona esférica o semiesférica, de acuerdo con la posición de la semicircunferencia. [br]9. Una figura genera un sólido diferente si cambia el eje de rotación.[br][br][/color][/color][/color]

 Es el sólido que se genera mediante la rotación completa de una región triángular alrededor de uno de sus catetos.[br][br][url=https://4.bp.blogspot.com/_q5Qjxleimr0/SvQ_1LONPFI/AAAAAAAAADk/R3148vPWd70/s1600-h/cono.png][img]https://4.bp.blogspot.com/_q5Qjxleimr0/SvQ_1LONPFI/AAAAAAAAADk/R3148vPWd70/s320/cono.png[/img][/url]

Es el sólido que se genera mediante una rotación de 360 grados de una región rectangular alrededor de uno de sus lados.[br][br][img]https://3.bp.blogspot.com/_q5Qjxleimr0/SvRs9QFrXTI/AAAAAAAAAFM/U0oNBlCk0Os/s1600/Cilindro_1.jpg[/img]

[img]http://3.bp.blogspot.com/_oN2saYz_C6Y/S8l4kQtSqII/AAAAAAAAAAc/1c-WOoMmP_A/s320/cilindro.gif[/img][img]http://4.bp.blogspot.com/_oN2saYz_C6Y/S8l897s9l0I/AAAAAAAAABE/52ucwD-o_Rw/s320/cilin.gif[/img][list=1][*]Cilindro: El volumen de un cilindro es el área de la base por la altura.[/*][/list][br][br][br][br]Consideremos un cilindro con radio de 4 centímetros y altura de 10 centímetros.[br][br][br][img]https://i2.wp.com/www.celeberrima.com/wp-content/uploads/2018/07/Ejemplo-y-f%C3%B3rmula-volumen-de-un-cilindro.jpg?resize=397%2C511&ssl=1[/img][br]Para hallar el volumen de nuestro cilindro utilizamos la fórmula:[img width=130,height=21]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D%5Cpi+%5Ccdot+r%5E2+%5Ccdot+h&bg=ffffff&fg=000&s=2[/img]Sustituyendo valores tenemos:[img width=301,height=30]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D3.1416+%5Ccdot+%5Cleft%284+%5Chspace%7B0.2cm%7D+%5Bcm%5D%5Cright%29%5E2+%5Ccdot+10+%5Chspace%7B0.2cm%7D+%5Bcm%5D&bg=ffffff&fg=000&s=2[/img][img width=368,height=25]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D3.1416+%5Ccdot+%5Cleft%284+%5Ccdot+4%5Chspace%7B0.2cm%7D+%5Bcm+%5Ccdot+cm%5D%5Cright%29+%5Ccdot+10+%5Chspace%7B0.2cm%7D+%5Bcm%5D&bg=ffffff&fg=000&s=2[/img][img width=295,height=26]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D3.1416+%5Ccdot+16+%5Chspace%7B0.2cm%7D+%5Bcm%5E2%5D+%5Ccdot+10+%5Chspace%7B0.2cm%7D+%5Bcm%5D&bg=ffffff&fg=000&s=2[/img][img width=217,height=26]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D3.1416+%5Ccdot+160+%5Chspace%7B0.2cm%7D+%5Bcm%5E3%5D&bg=ffffff&fg=000&s=2[/img][img width=170,height=26]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D502.656+%5Bcm%5E3%5D&bg=ffffff&fg=000&s=2[/img]

[img]http://2.bp.blogspot.com/_oN2saYz_C6Y/S8l7j8IzYFI/AAAAAAAAAAk/T-gZDi69nkc/s320/cono.gif[/img][list=1][url=http://4.bp.blogspot.com/_oN2saYz_C6Y/S8l8F-HxAGI/AAAAAAAAAAs/UpIaaLVvjps/s1600/cono1.gif][img]http://4.bp.blogspot.com/_oN2saYz_C6Y/S8l8F-HxAGI/AAAAAAAAAAs/UpIaaLVvjps/s320/cono1.gif[/img][/url][br][/list][list=1][*]Cono: El volumen de un cono es un tercio del área de la base por la altura. [/*][/list][b]Ejemplo:[/b]Podemos considerar un cono con radio de la base de 2 centímetros y una altura de 5 centímetros.[img width=541,height=721]https://i1.wp.com/www.celeberrima.com/wp-content/uploads/2018/07/Ejemplo-y-f%C3%B3rmula-volumen-de-un-cono.jpg?resize=541%2C721&ssl=1[/img]Para hallar el volumen de este cono utilizamos la fórmula:[img width=159,height=30]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot+%5Cpi+%5Ccdot+r%5E2+%5Ccdot+h&bg=ffffff&fg=000&s=2[/img]Sustituyendo valores se tiene que:[img width=319,height=32]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot+3.1416+%5Ccdot+%5Cleft%282+%5Chspace%7B0.2cm%7D%5Bcm%5D+%5Cright%29%5E2+%5Ccdot+5+%5Chspace%7B0.2cm%7D%5Bcm%5D&bg=ffffff&fg=000&s=2[/img][img width=386,height=30]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot+3.1416+%5Ccdot+%5Cleft%282+%5Ccdot+2+%5Chspace%7B0.2cm%7D%5Bcm+%5Ccdot+cm%5D+%5Cright%29+%5Ccdot+5+%5Chspace%7B0.2cm%7D%5Bcm%5D&bg=ffffff&fg=000&s=2[/img][img width=324,height=30]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot+3.1416+%5Ccdot+%5Cleft%284+%5Chspace%7B0.2cm%7D%5Bcm%5E2%5D+%5Cright%29+%5Ccdot+5+%5Chspace%7B0.2cm%7D%5Bcm%5D&bg=ffffff&fg=000&s=2[/img][img width=256,height=30]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot+3.1416+%5Ccdot+%5Cleft%2820+%5Chspace%7B0.2cm%7D%5Bcm%5E3%5D+%5Cright%29&bg=ffffff&fg=000&s=2[/img][img width=196,height=30]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot+62.832+%5Chspace%7B0.2cm%7D%5Bcm%5E3%5D&bg=ffffff&fg=000&s=2[/img][img width=167,height=26]https://s0.wp.com/latex.php?zoom=1.25&latex=V%3D20.944+%5Chspace%7B0.2cm%7D%5Bcm%5E3%5D&bg=ffffff&fg=000&s=2[/img]El volumen del cono resultó de 20.944 centímetros cúbicos.[br][br][br] [br][br][br] [br][br]