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How to Calculate the Mass of Sand

"A foolish consistency is the hobgoblin of little minds," said American philosopher Ralph Waldo Emerson, but the consistency of sand is what makes ocean beaches wonderful places to stroll and play on a summer afternoon. This consistency comes from the fact that fine beach sand is commonly composed of grains of mineral quartz (silicon dioxide, or SiO2) with an average diameter between 0.25 and 0.10 millimeters and a density of 2.65 grams per cubic centimeter. Find the mass of a grain of sand with a few simple calculations.

Things You'll Need

Pencil and paper
Calculator

Instructions

- 1
  Divide the average diameter of a grain of fine beach sand by two using a calculator. For example, 0.175/2 = 0.0875.
- 2
  Cube your answer using a calculator. For example, 0.0875 x 0.0875 x 0.0875 = 6.699 x 10^-4.
- 3
  Multiply your answer times pi, which is approximately equal to 3.1415. For example, 6.699 x 10^-4 x 3.1415 = 0.0021.
- 4
  Multiply your answer times 4/3. For example, 0.0021 x (4/3) = 0.0028. The volume of an average grain of fine beach sand is 0.0028 cubic centimeters.
- 5
  Multiply your answer times 2.65, the average density of sand. For example, 0.0028 x 2.65 = 0.0074 grams. The mass of an average grain of fine beach sand is 0.0074 grams.
- 6
  Multiply your answer times 1,000. For example, 0.0074 x 1000 = 7.43. The mass of an average grain of fine sand is 7.43 milligrams.

Rocks & Minerals