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Let $H$ be an $N$-dimensional rectangular with edges of length $L_i$, $i=1,2,\dots,N$. Is the volume simply the product of the $L_i$, $i=1,2,\dots,N$?

$$ \text{Volume} = L_1 \times L_2 \times \dots \times L_N$$

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  • $\begingroup$ Yes it is and the Volume is a kind of abstraction when $N\gt 3$. $\endgroup$
    – Piquito
    Sep 30, 2016 at 11:09

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This is an easy one. Short response: Yes

"Long" response: The volume of a region is just the integral of the function $f(x_1,x_2,x_3...)=1$ over the region. In the case of a n-rectangle

$$V=\int_R\text{d}x_1\text{d}x_2\dots=\int_{L_1}\text{d}x_1\int_{L_2}\text{d}x_2...=L_1\cdot L_2\cdot...$$

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