Question 1152546: An archaeologist finds a huge monolith in the desert. In order to estimate the mass of this object, he estimates the dimensions of the monolith and removes some chips from the rock with his hammer, collecting the following data:
dimensions of the monolith = 1.50 m × 5.20 m × 13.00 m
mass of rock chips = 41.73 g
volume of rock chips = 15.2 cm3
a) Determine the mass of the monolith in pounds, assuming it is of uniform composition (2.205 lbs = 1 kg).
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! dimensions of the monolith = 1.50 m × 5.20 m × 13.00 m
mass of rock chips = 41.73 g
volume of rock chips = 15.2 cm3
a) Determine the mass of the monolith in pounds, assuming it is of uniform composition (2.205 lbs = 1 kg).
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the volume of the monolith is equal to 1.5 * 5.2 * 13 = 101.4 cubic meters.
since 1 cubic meter is equal to 1 million cubic centimeters, then the volume of the monolith is equal to 101.4 million cubic centimeters.
the ratio of grams per cubic centimeter is equal to 41.73 / 15.2 = 2.745394737.
this ratio was taken from the rock chips.
based on this ratio, the monolith has a mass of 2.745394737 * 101.4 million cubic centimeters = 278.3830263 million grams.
since 1 kilogram is equal to 1000 grams, then the mass of the monolith is equal to 278.3830263 million / 1000 = 278.3830263 thousand kilograms.
since the mass in pounds is equal to 2.205 * the mass in kilograms, then the mass of the monolith is equal to 2.205 * 278.3830263 thousand kilograms = 623.834573 thousand pounds.
that should be your answer.
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you can do the same thing using scientific notation as shown below:
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the volume of the monolith is equal to 1.5 * 5.2 * 13 = 101.4 cubic meters.
since 1 cubic meter is equal to 1 million cubic centimeters, then the volume of the monolith is equal to 101.4 * 10^6 cubic centimeters.
the ratio of grams per cubic centimeter is equal to 41.73 / 15.2 = 2.745394737.
this ratio was taken from the rock chips.
based on this ratio, the monolith has a mass of 2.745394737 * 101.4 * 10^6 cubic centimeters = 278.3830263 * 10^6 grams.
since 1 kilogram is equal to 1000 grams, then the mass of the monolith is equal to 278.3830263 * 10^6 / 10^3 = 278.3830263 10^3 kilograms.
since the mass in pounds is equal to 2.205 * the mass in kilograms, then the mass of the monolith is equal to 2.205 * 278.3830263 * 10^3 kilograms = 623.834573 * 10^3 pounds.
that should be your answer.
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you can also do this using straight decimal format as shown below:
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the volume of the monolith is equal to 1.5 * 5.2 * 13 = 101.4 cubic meters.
since 1 cubic meter is equal to 1 million cubic centimeters, then the volume of the monolith is equal to 101,400,000 cubic centimeters.
the ratio of grams per cubic centimeter is equal to 41.73 / 15.2 = 2.745394737.
this ratio was taken from the rock chips.
based on this ratio, the monolith has a mass of 2.745394737 * 101,400,000 cubic centimeters = 278,383,026.3 grams.
since 1 kilogram is equal to 1000 grams, then the mass of the monolith is equal to 278,383,026.3 / 1000 = 278,383.0263 kilograms.
since the mass in pounds is equal to 2.205 * the mass in kilograms, then the mass of the monolith is equal to 2.205 * 278,383.0263 kilograms = 613,834.573 pounds.
that should be your answer.
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anyway you do it, the answer is, and should be, the same.
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