Formalising Technical Interrelationships - Example 6

The surface area of a circle is calculated with the following formula: .
Due to the fact that the surface area of the square amounts to A= 1 m ², the diameter D = 1m. With this information, the area which has to be multiplied by the number of circles, i.e. by n², can be calculated.

For n = 1 , the area A₁ is calculated as follows:
              

Therefore, for n = 2, the area A₂ is calculated as follows:  

For n = 4, the area A₄ is calculated as follows:

Finally, for n = 8, the area A₈ is calculated as follows:

The comparison of the four areas shows that: A₁ = A₂ = A₄ = A₈.

The correct solution is therefore D.