Question

aluminum is used to make airplanes and cast iron is used in weight lifting equipment.
Explain why the densities of these metals make them useful for these purposes.

Answer 1

This is mostly common sense based on what you know about planes and weight (e.g dumbells)

First know that the definition of density is: \(\sf \color{green}{ density=\dfrac{mass}{volume}}\)

Planes are built to fly, right? so they must be light, meaning that for a given volume, there shouldn't be much mass ( a lot of atoms) - low density.

what about weights? you want as compact of an object to focus the weight minimally, so you want lift a lot (if that's what you're into). so for a given volume, there should be a lot of mass - a high density.

look into sphere packing densities for more in depth stuff