Three Piles of Rice

Now a pile of rice is against the wall with a base circumference 60 chi and an altitude of 12 chi. What is the volume? Another pile is at an inner corner, with a base circumference of 30 chi and an altitude of 12 chi. What is the volume? Another pile is at an outer corner, with base circumference of 90 chi and an altitude of 12 chi. What is the volume?

Suanfa tongzong (Systematic Treatise on Mathematics), Cheng Dawei, 1592

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The answer is: each pile represents a portion of an identical cone, with the pile against the wall a half-cone with volume \(\dfrac{7200}{\pi} \approx 2292\) cubic chi, the pile in the inner corner a quarter-cone with volume \(\dfrac{3600}{\pi} \approx 1146\) cubic chi, and the pile at the outer corner a three-quarter-cone with volume \(\dfrac{10800}{\pi} \approx 3438\) cubic chi

"Three Piles of Rice," Convergence (June 2007)

Convergence