長方管體積
\[ \displaystyle \begin{aligned} &= \text{底面積} \times \text{長度}\\[6pt] &= \left( \text{外矩形面積} - \text{內矩形面積} \right) \times \text{長度} \\[6pt] &= \left( \text{外長} \times \text{外寬} - \text{內長} \times \text{內寬} \right) \times \text{長度} \\[6pt] &= \left[ \, \text{外長} \times \text{外寬} - \left( \text{外長} - 2 \times \text{長邊厚度} \right) \times \left( \text{外寬} - 2 \times \text{寬邊厚度} \right) \, \right] \times \text{長度} \\[6pt] &= \left( 2 \times \text{外長} \times \text{寬邊厚度} + 2 \times \text{外寬} \times \text{長邊厚度} - 4 \times \text{長邊厚度} \times \text{寬邊厚度} \right) \times \text{長度} \\[6pt] &= \left( 2 H t_B + 2 B t_H - 4 t_H t_B \right) L \end{aligned} \] 
