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SMO 2021 Junior Round 1 Question 17

SMO · SMO 2021 Junior Round 1

Question 17

The diagram below shows a piece of cardboard in the shape of an equilateral triangle with side length $36$ cm. Six perpendicular cuts of length $2\sqrt3$ cm are made to remove the corners in order to fold the cardboard into a tray whose base is an equilateral triangle and height is $2\sqrt3$ cm. What is the volume of the tray in cm$^3$?

Question illustration