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

ans)

from above data that

first we have to

calculate area of Michigan in meter²

1609.34 m = 1 mile

1 mile² = 2589975.23 m²

^{given that}  5.680 x 10⁴ mi²

5.680 x 10⁴ mi² = 5.680 x 10⁴ x 2589975.23 m²

= 1.47 x 10¹¹ m²

we know that the

area of 1 marshmallow = pid²/4

substitute above value in this equation

= 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

given height = 2.54 cm

we know that

avogadro's no marshmallow = 6.023 x 10²³

6.023 x 10²³ = n x4.65 x10¹⁵

Here n represents no. of layers

n = 1.29 x 10⁸ layers

given 1 layer = 2.54 cm

substitue all value in above

1.29 x 10⁸ layers = 2.54 cm x 1.29 x 10⁸ cm

= 3.27 x 10⁸ cm

= 3.27 x 10³ km

the height of the surface=3.27 x 10³ km

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