Question

Suppose you have Avogadro's number of mini marshmallows and use them to cover the state of South Dakota which has a land area of 7.588 × 10 4 mi 2 . 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

Answer: 2.44*10^3 km

Step-by-step explanation:

NOTE: We would be solving this question in "cm" instead of the usual "m"

1 mi² = 2.59 km²

2.59 km² = 2.59*10^10 cm²

Given, area of South Dakota

A = 7.588*10^4 mi²

A = 7.588*10^4 * 2.59*10^10

A = 1.97*10^15 cm² is the area of South Dakota

S = πd²/4

S = 3.142 * 0.635² / 4

S = 3.142 * 0.4/4

S = 3.142 * 0.1

S = 0.3142 cm² is the area of 1 marshmallow

1.97*10^15 / 0.3142 = 6.27*10^15, thus is the number of marshmallows in one single layer to cover the state area

6.02*10^23 / 6.27*10^15 = 9.6*10^7, this is the number of layers

9.6*10^7 * 2.54 = 2.44*10^8, this is the height in cm

Height in km is 2.44*10^3 km