Question

Suppose you have Avogadro's number of mini marshmallows and use them to cover the state of Michigan which has a land area of 5.680 × 104 mi2. Each mini marshmallow has a diameter of 0.635 cm and a height of 2.54 cm. 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

lets calculate area of Michigan in meter²

1609.34 m = 1 mile

1 mile² = 2589975.23 m²

5.680 x 10⁴ mi² = 5.680 x 10⁴ x 2589975.23 m² = 1.47 x 10¹¹ m²

area of 1 marshmallow = pid²/4 = 3.14 x (0.00635 m)² = 3.16 x 10^-5 m²

assumed no. gap , total marshmallow needed to cover =1.47 x 10¹¹ m² / 3.16 x 10^-5 m²

= 4.65 x10¹⁵ marshmallows

this is 1 layer and having height = 2.54 cm

and we have avogadro's no marshmallow = 6.023 x 10²³

6.023 x 10²³ = n x4.65 x10¹⁵

n represents no. of layers

n = 1.29 x 10⁸ layers

1 layer = 2.54 cm

1.29 x 10⁸ layers = 2.54 cm x 1.29 x 10⁸ cm = 3.27 x 10⁸ cm = 3.27 x 10³ KM !!

we have to use it all !!!

6.023 x 10²³ -