How to Determine a Cube and Sphere of Equal Volume

Step-by-Step Guide

1. 1

   Step 1: Set V(c) = V(s) via r1^3 = 4/3πr2^3;

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   Step 2: r1^3/r2^3 = 4/3π by dividing both sides by r2^3 and simplifying.

3. 3

   Step 3: r1/r2 = (4/3π)^(1/3) = 1.61199195401647 by taking the cube root of both sides and evaluating the right side in Excel as "=(4/3*PI())^(1/3)"

4. 4

   Step 4: Now we can find either r1 or r2 given the other one

5. 5

   Step 5: for r1 = r2 * 1.61199195401647 and r2 = r1 / 1.61199195401647

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   Step 6: where r2 is the radius of the sphere and r1 is the side of the cube.

7. 7

   Step 7: We now have also learned that (4/3π)^(1/3) MEANS the constant of proportion of the volume of a cube equal in volume to a sphere of different basis length r.

8. 8

   Step 8: Make use of helper articles when proceeding through this tutorial: See the article How to Determine a Square and Circle of Equal Perimeter for a list of articles related to Excel

9. 9

   Step 9: Geometric and/or Trigonometric Art

10. 10

    Step 10: Charting/Diagramming and Algebraic Formulation.

Detailed Guide

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