Nice's central library building is considered one of the most original in the world, as it is a mix between a sculpture and a work of habitable architecture. It was called La Tête Carrée and is made up of part of a bust that supports a cube divided into five floors. It is known that the building has a total height of approximately 30 meters. It admits that the cubic part of the sculpture is parallel to the floor and has a volume of 2744 meters3 Calculate, in meters, the height of the bust that supports the cube. Displays all the calculations you made.

Let the height of the bust be represented by 'h' meters.

The volume of a cube is given by the formula V = s^3, where 's' is the length of the side of the cube.
In this case, we are given that the volume of the cube is 2744 meters^3.
So, we can write the equation as 2744 = s^3.

We also know that the total height of the building is 30 meters. The height of the bust (h) plus the height of the cube (s) should add up to the total height.
So, we can write another equation as h + s = 30.

Now, we can solve these two equations to find the values of 'h' and 's'.

From the equation 2744 = s^3, we take the cube root on both sides to get:
s = ∛2744.

Using a calculator, we find that the cube root of 2744 is 14.

Now, substituting the value of 's' in the equation h + s = 30, we have:
h + 14 = 30.

Subtracting 14 from both sides of the equation, we get:
h = 30 - 14 = 16.

Therefore, the height of the bust that supports the cube is 16 meters.

Answer: The height of the bust is 16 meters.