《孫子算經卷中》 "Sun Tzŭ's Computational Classic: Volume II"
§18. Volume of a rectangular prism (2)

This section gives a worked example of computing the volume of a rectangular prism.

The relevant unit conversion for length is

1 \unit{rod~(丈)} = 10 \unit{rules~(尺)}.

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text	Target text	Notes
今有溝、廣十丈、深五丈、長二十丈、欲以千尺作一方。問得幾何。	Suppose there be [a] ditch, of breadth ten rods, depth five rods, [and] length twenty rods, [and we] wish to use [a] thousand rules doing one block. [We] ask, how many result?
答曰、一千方。	Answer saith: one thousand blocks.
術曰、置廣一十丈。以深五丈乘之、得五千尺。又以長二十丈乘之、得一百萬尺。	Method saith: put [down the] breadth ten rods. Multiplying it by [the] depth five rods, resulteth in five thousand rules. And multiplying it by [the] length twenty rods, resulteth in one hundred myriad rules.
以一千除之、即得。	Dividing it by one thousand, [we] are done.	In modern notation, the volume of a rectangular prism of breadth B = 10 \unit{rods}, depth H = 5 \unit{rods}, and length L = 20 \unit{rods} is \begin{aligned} V &= B H L \\ &= 100 \unit{rules} \times 50 \unit{rules} \times 200 \unit{rules} \div \frac{1000 \unit{rules}^3}{\unit{block}} \\[\tallspace] &= 1000 \unit{blocks}. \end{aligned}

Conway (2023). "Sun Tzŭ's Computational Classic: Volume II §18". <https://yawnoc.github.io/sun-tzu/ii/18> Accessed yyyy-mm-dd.