Description.. Alaska has an area of...

Question

Suppose you have Avogadro's number of mini marshmallows and use them to cover the state of Alaska which has a land area of 5.720 x 10^5 mi^2 Each mini marshmallow has a diameter of 0.635 cm and a height of 2.54cm. Assuming the marshmallows are packed together so there is no space between them, to what height above the surface, in kilometers, will the mini marshmallows extend?

Answer 1

Assume the marshmallows maintain their cross-sectional area when mushed together (not correct but you have to assume something, since the question implies that there is no space between them. You could also assume that the marshmallows area is circular and that they touch like circles inscribed in squares with the side equal to the diameter of the circle. Finally you could assume that they are close-packed like oranges on display which is the packing that wastes the least area). This looks like a units problem, so I assume you are to keep things as basic as possible (so 1st assumption)):

Calculate the area of a marshmallow: A = πd²/4

The Area of a mole of marshmallows A_T = N_AA where N_A is Avogadro's numbjer

You have to make the length and area and volume units the same, so, km makes sense in order to get an answer in km...

Alaska's area is 5.720 x 10⁵ mi² x (1.609 km/1 mile)²

The area total is A_T x (1 km/10⁵cm)²

To find how many layers of marshmallows up you will need take A_T/A_Alaska

How high will that be" Round the number of tiers up to the highest integer and multiply by 2.54 cm (1km/10⁵cm)

If you make the 2nd or third assumption, you can calculate the wasted space in going from circle to square. The height will increase as a resul, because you use fewer marshmallows for a given area.