Name: pappus and guldinus theorems for surface area
Uploaded: 2023-09-22T11:49:32.000Z
Duration: 1 min 12 s
Channel: JoVE

Considere un tanque de almacenamiento cilíndrico con una tapa cónica. 
El tanque representa un cuerpo compuesto, que se puede dividir en un número finito de partes con formas más simples.
Los teoremas de Pappus y Guldinus se pueden aplicar para encontrar el área de superficie y el volumen de tales formas compuestas.
Para encontrar el área de superficie, se identifican las curvas generadoras de cada forma y se giran alrededor de un eje que no se intersecta. A continuación, se ubica el centroide para cada curva.
La longitud de la curva generadora y la distancia recorrida por el centroide de la curva se utilizan para obtener el área de superficie total del tanque.
Del mismo modo, para estimar el volumen, se identifica el área generadora de cada forma y se gira alrededor del mismo eje.
El volumen de un cuerpo de revolución es igual al producto del área generadora y la distancia recorrida por el centroide de la figura.
Al encontrar el área de cada parte e identificar sus respectivos centroides, los valores se sustituyen en el teorema para obtener el volumen del tanque.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica: Estática. Decimocuarta edición, Nueva Jersey: Pearson. Sección 9.3, págs. 503 y 507.</li>
</ol>

los teoremas de pappus y guldinus: resolución de problemas

Los teoremas de Pappus y Guldinus son poderosos principios matemáticos que se utilizan para encontrar el área superficial y el volumen de formas compuestas. Por ejemplo, consideremos un tanque de almacenamiento cilíndrico con una parte superior cónica. Encontrar el área superficial o el volumen puede ser desafiante para formas tan complejas. Estos teoremas son particularmente útiles para calcular el volumen y el área superficial de tales sistemas. Aquí, el tanque de almacenamiento cilíndrico con una parte superior cónica se puede descomponer en dos formas simples: un cilindro y un cono. Para resolver este problema, se aplica el primer teorema para encontrar el área superficial del sólido formado al girar cada una de las curvas generadoras alrededor de un eje no intersecante. Esto implica sustituir valores relevantes como la longitud de la curva generadora y la distancia recorrida por su centroide, obteniendo valores separados para cada parte y luego sumándolos para obtener un total general. Para calcular el volumen, giramos un área alrededor del mismo eje que antes y utilizamos información del segundo teorema, que implica multiplicar las áreas generadas por las distancias recorridas por sus respectivos centroides. Al realizar cálculos con estos dos principios, se vuelve más fácil encontrar valores precisos tanto para el área superficial como para el volumen de formas complejas como este tanque de almacenamiento.

Los teoremas de Pappus y Guldinus: Resolución de problemas

Los teoremas de Pappus y Guldinus son poderosos principios matemáticos que se utilizan para encontrar el área superficial y el volumen de las formas compuestas. Para...

theorems-of-pappus-and-guldinus-problem-solving

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Unit 1

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Center of Gravity and Centroid

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Theorems of Pappus and Guldinus: Problem Solving

pappus and guldinus theorems for surface area

Pappus and Guldinus's theorems help find the surface area and volume of composite shapes. These rules are useful when a solid is made from simple parts that are hard to measure directly. A cylindrical storage tank with a conical top is one example.

The tank can be split into two simple shapes: a cylinder and a cone. To find surface area, the first theorem is used for the solid formed by revolving each generating curve around a non-intersecting axis. The calculation uses the length of the generating curve and the distance traveled by its centroid, or center of mass.

The surface area is found separately for each part and then added together. To find volume, the second theorem is used. It works by revolving an area around the same axis and multiplying the generated area by the distance traveled by its centroid. This makes it easier to calculate accurate surface area and volume for complex shapes like the storage tank.

Pappus and Guldinus Theorems for Surface Area

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Pappus and Guldinus theorems help find the surface area and volume of bodies of revolution. A body of revolution is formed when a plane curve or plane area is turned around an axis that does not intersect it. For surface area, a curve is revolved around a non-intersecting axis. A small line element on the curve creates a thin ring as it moves. Adding these ring areas gives the total surface area of the solid. The first theorem says that this surface area equals the length of the generating...

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Learn how Pappus and Guldinus's theorems help calculate surface area and volume for composite shapes like a tank with a conical top.

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Pappus and Guldinus Theorems for Surface Area

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