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When a cube is sliced by a plane perpendicular to one of its diagonals, what is the shape of the resulting cross-section ?

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  1. Hexagon
  2. Pentagon
  3. Octagon
  4. Trapezoid

Answer (Detailed Solution Below)

Option 1 : Hexagon
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Detailed Solution

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Given:- When a cube is sliced by a plane perpendicular to one of its diagonals.

Step 1: Understanding the Geometry:- The cube has 12 edges, 8 vertices, and 6 faces. When a plane intersects the cube, it can create various shapes depending on the angle and position of the plane.

Step 2: Identifying the Diagonal:- A diagonal of a cube connects two opposite vertices and passes through the interior of the cube. There are 4 diagonals in a cube.
 
Step 3: Plane Perpendicular to the Diagonal:- A plane perpendicular to a diagonal will intersect the cube in such a way that it cuts through the diagonal at a right angle.
 
Step 4: Shape of the Cross Section:- When a plane is perpendicular to a diagonal of the cube, it will intersect three pairs of parallel edges of the cube. This intersection results in a hexagon.

Hence, The correct answer is option 1. 

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