How do I Compute the Density of a Sphere?
- 1). Determine the mass, m, of the sphere. For a density word problem, such as from a science textbook, the mass of the object should be stated in the problem. If the density of a sphere is to be determined experimentally, then the sphere must be weighed on a balance. By scientific convention, the mass should be measured in units of grams or kilograms.
- 2). Determine the volume of the sphere. Again, a word problem may state the volume outright, or it may provide measurement data for radius, diameter, or circumference. If performing an experiment, measure the diameter with a set of calipers or, alternatively, with a ruler. Length measurements are stated typically in units of centimeters or meters.
- 3). Calculate the volume of the sphere. The exact formula depends on the data available. The general equation for the volume (V) of a sphere is V = 4/3 * pi * r^3, where pi = 3.14159... and r is the sphere's radius, preferably in centimeters. Note also that r = 0.5d, where d is the sphere's diameter. Combining these various equations provides two equations for the volume of a sphere:
If working from radius, V = 4/3 * pi * r^3;
If working from diameter, V = 4/3 * pi * (0.5d)^3.
If, for example, the sphere exhibited a diameter of 2.5 cm, then
V = 4/3 * 3.14159 * (0.5 * 2.5 cm)^3 = 4/3 * 3.14159 * (1.3 cm)^3 = 8.2 cm^3. - 4). Calculate the sphere's density according to d = m / V using the results from Steps 1 and 3. If the sphere from step 3 exhibited a mass of 55 grams, then
d = m / V = 55 g / 8.18 cm^3 = 6.7 g/cm^3.
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