Find the formula for the volume of a solid - Сообщения
#1 Опубликовано: 16.10.2026 11:26:33
Consider a solid bounded by a surface formed by the intersection of seven cylinders of radius $R$. The axes of these cylinders all intersect at a single point; four of the axes are directed along the long diagonals of a cube, while the remaining three are perpendicular to the faces of the cube
Look at the image.
Look at the image.
#2 Опубликовано: 16.10.2026 21:34:13
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Вячеслав Мезенцев 17.10.2026 02:12:08
#3 Опубликовано: 17.10.2026 04:56:07
Alvaro, thank you. Unfortunately, your calculation method results in a 4.5 percent error relative to the true volume of the object.
(The layer thickness turned out to be a bit too small.
(The layer thickness turned out to be a bit too small.
#4 Опубликовано: 17.10.2026 13:35:37
Alvaro, the discussion concerned obtaining an exact formula. Look up "Steinmetz solid" on Wikipedia. Your approximate formula does not account for the volume of the parts cut off from the solid.
See the image
See the image
#5 Опубликовано: 17.10.2026 18:29:06
Hi Victor. The procedure looks good enough to me for the others cases.
Steinmetz Solid.pdf
Steinmetz Solid.sm
Best regards
Alvaro.
Steinmetz Solid.pdf
Steinmetz Solid.sm
Best regards
Alvaro.
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