# Surface Area of a Molecule

Geometry Level 4

A new molecule $$\ce{A2Z}$$ has been discovered. It is made of two atoms of $$\ce{A}$$ and one atom of $$\ce{Z}$$. 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 $$\ce{A2Z}$$ molecule is $$S \text{ pm}^2$$, then what is $$\dfrac{S}{\pi}$$?

Details and Assumptions

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

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

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

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

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