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Línea 20: | Línea 20: | ||
<math> | <math> | ||
{A_{saco} = \color{Green}{L_v} \times \color{Green}h}</math> | {A_{saco} = \color{Green}{L_v} \times \color{Green}{h}}</math> | ||
[[Archivo:sección_saco_semicírculo.png]] | [[Archivo:sección_saco_semicírculo.png]] | ||
<math> | <math> | ||
A_{saco} = \left(\color{Green}L_v - \dfrac{\pi \color{Green}h}{2} \right) \times \color{Green}h + \pi \left(\dfrac{\color{Green}h}{2}\right)^2 = \color{Green}L_v \color{Green}h - \dfrac{\pi \color{Green}h^2}{4} | A_{saco} = \left(\color{Green}{L_v} - \dfrac{\pi \color{Green}{h}}{2} \right) \times \color{Green}{h} + \pi \left(\dfrac{\color{Green}{h}}{2}\right)^2 = \color{Green}{L_v} \color{Green}{h} - \dfrac{\pi \color{Green}{h}^2}{4} | ||
</math> | </math> | ||
Línea 31: | Línea 31: | ||
<math> | <math> | ||
\sin \alpha = \dfrac{\dfrac{h}{2}}{h} = \dfrac{1}{2}; \alpha = 30^\circ | \sin \alpha = \dfrac{\dfrac{\color{Green}{h}}{2}}{\color{Green}{h}} = \dfrac{1}{2}; \alpha = 30^\circ | ||
\\ | \\ | ||
\begin{align} | \begin{align} | ||
A_{saco} & = \left(L_v - \dfrac{\pi h}{3} \right) \times h + 2 \left(\pi h^2 \times \dfrac{2\alpha}{360} - \dfrac{1}{2} \times h \sqrt{h^2 - \left(\dfrac{h}{2} \right)^2} \right) \\ | A_{saco} & = \left(\color{Green}{L_v} - \dfrac{\pi \color{Green}{h}}{3} \right) \times \color{Green}{h} + 2 \left(\pi \color{Green}{h}^2 \times \dfrac{2\alpha}{360} - \dfrac{1}{2} \times \color{Green}{h} \sqrt{\color{Green}{h}^2 - \left(\dfrac{\color{Green}{h}}{2} \right)^2} \right) \\ | ||
& = L_v h - \dfrac{\pi h^2}{3} + 2 \left(\pi h^2 \times \dfrac{1}{6} - \dfrac{1}{2} \times \dfrac{h^2 \sqrt{3}}{2} \right) \\ | & = \color{Green}{L_v} \color{Green}{h} - \dfrac{\pi \color{Green}{h}^2}{3} + 2 \left(\pi \color{Green}{h}^2 \times \dfrac{1}{6} - \dfrac{1}{2} \times \dfrac{\color{Green}{h}^2 \sqrt{3}}{2} \right) \\ | ||
& = L_v h - \dfrac{\pi h^2}{3} + \dfrac{\pi h^2}{3} - \dfrac{h^2 \sqrt{3}}{2} \\ | & = \color{Green}{L_v} \color{Green}{h} - \dfrac{\pi \color{Green}{h}^2}{3} + \dfrac{\pi \color{Green}{h}^2}{3} - \dfrac{\color{Green}{h}^2 \sqrt{3}}{2} \\ | ||
& = L_v h - h^2 \dfrac{\sqrt{3}}{2} | & = \color{Green}{L_v} \color{Green}{h} - \color{Green}{h}^2 \dfrac{\sqrt{3}}{2} | ||
\end{align} | \end{align} | ||
</math> | </math> |