The corner of a unit cube is chopped off such that the cut runs through the three vertices adjacent to the vertex of the chosen corner. What is the height of the remaining cube when the freshly-cut face is placed on a table?
+1490 The corner of a unit cube is chopped off such that the cut runs through the three vertices adjacent to the vertex of the chosen corner. What is the height of the remaining cube when the freshly-cut face is placed on a table?
Let the area of a single side of the cube be A = 25 cm².
The length of the edge is E = 5 cm
Let D be diagonal of a side of the cube. D = 5 / sin(45°) = 7.071067812
Angle after cutting the corner is: tan(β) = E / (D/2) β = 54.7356°
The height of the remaining cube is H = D * sin(β) = 5.7735 cm 
