Surface Area of a Molecule

Geometry Level 5

A new molecule AX2Z \ce{A2Z} has been discovered. It is made of two atoms of A \ce{A} and one atom of Z \ce{Z}. The surface area of a molecule can tell us loads about the chemical and physical properties of the molecule, hence it is imperative that we calculate it.

If the surface area of an AX2Z\ce{A2Z} molecule is S pm2 S \text{ pm}^2, then what is Sπ \dfrac{S}{\pi} ?

Details and Assumptions

  • We can model the molecule as three overlapping spheres as shown in the animation. The white spheres are atoms of A \ce{A} and the red sphere is an atom of Z\ce{Z}

  • The radius of Sphere A \ce{A} is 40 pm

  • The radius of Sphere Z \ce{Z} is 60 pm

  • The distance between the centers of Sphere A\ce{A} and Sphere Z\ce{Z} is 80 pm

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