The Department of Mathematics Education. EMAT 6700 J. Wilson

How do the Surface Area and Volume of Spheres Compare?

by: Scott Burrell and Kimberly Young

 

The surface area of a sphere can be calculated using the following formula, where r is the radius of the sphere

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The volume of a sphere can be calcuated using the following formula, where r is the radius of the sphere

In order to compare the surfrace area and volume of a sphere, we are going to look differnt radius values of balls.

 

Type of Ball Radius (in inches)
Ping-pong Ball 0.74
Golf Ball 0.84
Billard Ball 1.13
Tennis Ball 1.26
Baseball 1.47
Bowling Ball 4.29
Basketball 4.72

Calculate the surface area and volume for the above spheres, using Microsoft Excel. Next, use your graphing tool to graph the surface area and volume on the same axis.

Use the above graph to begin making conjectures about how the surface area and volume are affected by the radius of a sphere. Is there a point when the surface area and volume will be the same? Is the surface area always greater than the volume of a sphere?

 

Suggestion: Use graphing calculator to investigate these questions further. Click Here

Click Here for the Excel file.

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