Brain Teaser

Consider the two shapes inside the two identical cylinders whose radius is equal to its height.

The volume on the left is a regular cone inscribed in the cylinder. The volume on the right is formed by subtracting an inscribed hemisphere from the cylinder.

When cut horizontally at the same height from the bottom, which cross-section has a larger area, the red or the green one?



  • The orange cross-section is larger.
  • The green cross-section is larger.
  • The cross-sections have the same area.
  • The relationship changes depending on the height of the slice.
  • Problem by BRILLIANT
  • Solution by David Vreken
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