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Evaluación sobre el volumen de la esfera

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Evaluación sobre el volumen de la esfera

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aprendizaje y enseñanza del volumen de las esferas

Created by

Jefferson Guancha
Jefferson Guancha
Ecuador

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Evaluación sobre el volumen de la esfera
 

Evaluación sobre el volumen de la esferaOnline version

aprendizaje y enseñanza del volumen de las esferas

by Jefferson Guancha
1

¿Cuál es el primer paso esencial al resolver un problema de optimización de un sólido inscrito en una esfera?

2

En el contexto de la primera derivada, ¿qué representa físicamente un punto donde V'(x) = 0?

3

Para un cilindro inscrito en una esfera de radio R, ¿cuál es la relación pitagórica correcta entre su radio r y su altura h?

4

Al maximizar el volumen de un cilindro inscrito en una esfera de radio R, se obtiene que la altura óptima es:

5

¿Qué ocurre con el volumen de una esfera si su radio se duplica, según su fórmula de volumen?

Explicación

Necesitamos conectar las dimensiones del cuerpo inscrito con el radio constante para poder expresar la función en términos de una sola variable.

Cuando la pendiente de la recta tangente es horizontal, la función alcanza un extremo relativo antes de cambiar de dirección.

El triángulo rectángulo se forma desde el centro de la esfera hasta el borde del cilindro, usando la mitad de su altura.

Este resultado surge de derivar la función de volumen respecto a la altura e igualar a cero.

Al sustituir $2r$ en $r^3$, obtenemos $(2)^3 = 8$, por lo que el volumen crece por un factor de ocho.

 
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