Question

The sculpture ‘Cubo Vazado’ [Emptied Cube] by the Brazilian artist Franz Weissmann is formed by removing cubical blocks from a solid cube to leave the symmetrical shape shown.

If all the edges have length 1, 2 or 3, what is the volume of the sculpture?

Answer 1

The volume of the sculpture is 12 cubic units

Explanation:

The picture of the question in the attached figure

step 1

Find the volume of the L-shaped figure

The volume is given by

`V=Bh`

where

B is the area of the base

h is the height of the figure

we have

`h=1\ units`

The area of the base B is equal to the area of the complete square (3 units by 3 units) minus the area of the interior square (2 units by 2 units)

`B=3^2-2^2=5\ units^2`

so the volume of the L-shaped figure is equal to

`V=(5)(1)=5\ units^3`

step 2

Find the volume of the sculpture

we know that

The volume of the sculpture is equal to the volume of the L-shaped figure, multiplied by two plus the volume of two unit cubes

so

`V=2(5)+2(1)=12\ units^3`