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course MTH 173
5/12 1AM
Solve using proportionalities by stating the appropriate proportionality law and finding the proportionality constant:If a sand pile 2.7 meters high has a mass of 11022.48 kg, then what would we expect to be the mass of a geometrically similar sand pile 6.2 meters high?
If there are 3.3534 billion grains of sand exposed on the surface of the first sand pile, how many grains of sand we expect to be exposed on the surface of the second?
SOLUTION:
2.7x = 11022.48
x = 4082.4k
x = 4082.4(6.7)
x = 27352.08 kg
Proportionality constant: 4082.4 kg
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This is not a direct proportionality. Mass is not proportional to just the height of geometrically similar sandpiles.
Nor is the proportionality below correct.
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2.7x = 3.3534
x = 1.242k
x = 1.242(6.7)
x = 8.3214 billion grains of sand
Proportionality constant: 1.242 billion grains of sand"
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