How to Determine Equal Cube and Sphere Surfaces

Step-by-Step Guide

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   Step 1: Open a New Workbook and select the Media Browser tool

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   Step 2: Shapes option

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   Step 3: and create the diagram above.

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   Step 4: Set 6s^2 = 4πr^2

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   Step 5: Gather the numbers on the left and the variables on the right: 6/(4π) = r^2 / s^2

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   Step 6: Take the square root of both sides of the equation: sqrt(6/(4π)) = sqrt(r^2 / s^2) = r/s

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   Step 7: Evaluate the left side: sqrt(6/(4π)) =sqrt(6/(4*PI())) in MicroSoft Excel = 0.690988298942671

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   Step 8: or .691 approximately.

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   Step 9: .691= r/s so .691 * s = r and s = r/.691 and given one

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    Step 10: we can always find the other that will bring the two equal now.

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    Step 11: For example

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    Step 12: if side s = 1

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    Step 13: then 6s^2 = 6.000 and radius r = 1*.691

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    Step 14: so 4πr^2 = 6.0002

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    Step 15: which should be close enough for most purposes.

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    Step 16: Think of the advantages to Nature of creating cubes vs. spheres

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    Step 17: and vice versa;

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    Step 18: Make use of helper articles when proceeding through this tutorial: See the article How to Determine a Cube and Sphere of Equal Volume for a list of articles related to Excel

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    Step 19: Geometric and/or Trigonometric Art

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    Step 20: Charting/Diagramming and Algebraic Formulation.

Detailed Guide

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