SC 130 Physical science practical laboratory six 26 September 2008

Nature is an infinite sphere of which the center is everywhere and the circumference nowhere. - Blaise Pascal, Pensées

An attempt at visualizing the Fourth Dimension: Take a point, stretch it into a line, curl it into a circle, twist it into a sphere, and punch through the sphere. - Albert Einstein

To the first order of magnitude, a cow is a sphere. - Anonymous stellar astrophysics professor

Spheres are the mathematical name of three-dimensional shapes where the surface is a constant radius r from a center point. This laboratory explores the relationship between the radius and volume for spheres. The laboratory is very basic and simple. Your task is to design your own tables, make an appropriate graph, and run an analysis on the data. You should also do research to try to determine what theoretic values can be used to determine the error, if any, in your calculations.

Materials

• marbles, golf ball, other spheres that sink in water
• rulers
• graduated cylinders

Procedure

The following procedure refers to a duck marble. The procedure applies to any other sphere in the laboratory.

1. Measure the diameter of marble.
   
2. Calculate the radius of each marble. The radius is half the diameter.
3. Calculate the cube of the radius r³ of each marble.
4. Fill the appropriate sized cylinder for the marble half-way with water.
5. Note the exact volume of water in the cylinder by noting the value at the bottom of the meniscus. The meniscus is the curved shape water forms in a glass cylinder. In the image below the volume is 20 milliliters.
   
6. Gently place the marble in the cylinder. Note the new volume of water in the cylinder.
   
7. Calculate the volume of the marble by subtracting the volume before from the volume after. In the above images the volume increased by two milliliters, therefore the volume of the marble is two milliliters.
8. Repeat for each different size of marble, golf ball, or other sphere in the laboratory.

Data tables [d] [t]

Design your own data tables that report the name of the sphere measured, the diameter in centimeters, the radius in centimeters, the cube of the radius, and the volume of the sphere in milliliters.

Data display: Graph [g]

Make a graph using an appropriate graph type to display the mathematical relationship, if any, between the cube of the radius r³ and the volume in milliliters.

Data analysis [a]

The analysis should include answers to the following questions:

• Does the data appear to be modeled by a linear mathematical relationship?
• If not linear, is there a pattern? OR
• If linear, should you use LINEST or SLOPE and INTERCEPT? WHY?
• If linear, calculate either the LINEST or SLOPE and INTERCEPT, whichever you judge to be more appropriate.
• If linear, make a best effort to determine what the slope should be theoretically. If you determine a theoretic value for the slope, use that to determine your percentage error.

Conclusion [c] [f] [GVOC]

Wrap up with a conclusion that discusses whether there is a mathematical relationship and, if so, then the nature of that relationship. If you found a theoretic value, explain how you found that value. Discuss the error, if any, between your slope and the theoretic value. Write well. Grammar, vocabulary, organization, and cohesion will still be marked.