A substance's weight is directly related to its volume by its density. If you know the density of a substance and the volume you want to measure, you can calculate its weight.
Density, Mass and Weight
The relationship between mass, m, volume, V, and density, p, is shown by the following equation: p = m / V. For instance, the density of water is 1 gram for each cubic centimeter, or 1.0 gram / c^3. This means that each cubic centimeter of water will have a mass of 1 gram. At sea level, the weight of a substance is equal to its mass, so each cubic centimeter of water will have a weight of 1 gram.
Calculating the Weight of Lead
Suppose you want to calculate the weight of 250 cubic centimeters of lead at sea level. Lead has a density of 11.3 grams / c^3. Since: p = m / V, you also can say that m = Vp. So, multiply the volume of lead by its density, as follows:
m = 250 c^3 x 11.3 grams / c^3, or 2,825 grams
So, 250 cubic centimeters of lead will have a weight of 2,825 grams at sea level.
Check Your Units
When you calculate weight by volume, ensure that the units of volume you use match the units of volume in the density measurement. For example, if you want to weigh 25 cubic inches of lead, convert the volume from cubic inches into cubic centimeters first.
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