01/23/03

Title: Measuring the Volume of a Sphere

Materials: 1 plastic/glass globe with a hole (Christmas tree ball ornament), string, meter

stick, water, graduated cylinder, scale

where r is the radius of the sphere. Because density P = M/V, the volume of a sphere

could be calculated if the mass of the volume of water within the sphere was measured.

radius was determined. This radius could be approximated by measuring the

circumference of the sphere at its widest cross-section and then calculating the radius

using the relationship: circumference C = 2 ¹ r. The 2 calculated volumes were then

compared with the theoretical volume to find the percent error. The theoretical volume

was determined by measuring the volume of water inside the sphere by pouring it into a

graduated cylinder. The theoretical volume was measured to be 153 ml. The 2

calculated volumes were also compared to find the percent difference.

Procedure: The glass globe (Christmas tree ornament) was rinsed out. The mass was

measured on a scale and determined to be 9.33 g. The mass of a Styrofoam cup (which

would be used to hold the globe upright when it was filled with water) was measured on a

scale and determined to be 6.76 g. The globe was then filled with water to the base of its

"spout." It was carefully placed in the Styrofoam cup. The cup and globe containing

water were then placed on the scale and the total mass was determined to be 166.71 g.

The masses of the cup and globe were then subtracted from the total mass to calculate the

mass of the water which was determined to be 150.62 g. Density is given by the

relationship P = M/V. Density of water is assumed to be 1.00 g/ml, thus the experimental

volume of the sphere was calculated to be 150.62 ml.

Next, the water in the sphere was carefully poured into a graduated cylinder to determine

the actual volume and was measured to be 153.0 ml.

Finally, the circumference of the sphere was measured using a piece of string and a meter

stick. The string was wrapped around the largest cross sectional area of the sphere and

marked. The marked string was then straightened and measured with a meter stick. The

circumference was thus measured to be 21.0 cm. The circumference of a circle is given

by the relationship C = 2 ¹ r. The radius can thus be calculated as r = C/2 ¹ and was

determined to be 3.34 cm. It was assumed that the volume of a sphere is given by the

Results: The data for the experiment is given in a table below:

Percent error = [(Experimental Volume — Actual Volume)/Actual Volume] x 100%

Percent difference 3.6%

Conclusion: The results of this experiment were as predicted. The percent error in both

trials was relatively small considering the equipment used and the sources for error. The

measurements were taken fairly roughly and great care was not taken in precision. The

basic idea of the experiment was evident in the results. The sources of error in the first

trial were in the amount of water in the globe and in the way in which the water was

weighed. The water had to be filled exactly to the point below the base of the "spout" or

hole in the globe so that it occupied exactly the volume of the sphere, not more or less.

In the second trial, the way in which the circumference was measured was not exact. It

was impossible to determine the exact location of the largest cross-sectional area. When

comparing the results of the 2 trials, it is evident that the first trial measured the internal

volume of the sphere, where the second trial measured the external volume of the sphere.

The thickness of the glass would create differences in the 2 measurements for volume.

Finally, the actual volume of the water inside the sphere was not measured with extreme

precision as a 25 ml graduated cylinder was used. By filling the cylinder 7 times, there

were many opportunities to create error in measurement.