Image solid from development view /

Find the volume of the solid which is made by assembling the development view of the figure.

Each triangular face is an equilateral triangle.

Each face of a hexagon is a made figure where one side cuts out two right-angled isosceles triangles whose equal lengths of two sides are 1 cm from the square which is 2 cm one side.

Answer

22/3 cm³

Solution

It is required to surmise that this solid is made by cutting off four corners of the cube with 2cm one side based on the statement that there are six hexagon faces in the development as a hint to solve this problem.

As shown in a figure, the solid which is made by assembling this developed view becomes what cut out the triangular pyramid from four corners of the cube wit 2cm one side.

Therefore, the volume of this solid is 2 × 2 × 2 - 1 × 1 × 1/2 × 1 × 1/3 × 4 = 8 - 23 = 22/3cm³.