A cube & a Sphere have same surface area. Find the ratio of their volumes. || VSA HOTS CBSE 3
How to Determine Equal Cube and Sphere Surfaces
Open a New Workbook and select the Media Browser tool, Shapes option, and create the diagram above.
Set 6s^2 = 4πr^2
Gather the numbers on the left and the variables on the right:6/(4π) = r^2 / s^2
Take the square root of both sides of the equation:sqrt(6/(4π)) = sqrt(r^2 / s^2) = r/s
Evaluate the left side:sqrt(6/(4π)) =sqrt(6/(4*PI())) in Microsoft Excel = 0.690988298942671, or .691 approximately.
Thus, .691= r/s so .691 * s = r and s = r/.691 and given one, we can always find the other that will bring the two equal now.Problem solved.
For example, if side s = 1, then 6s^2 = 6.000 and radius r = 1*.691, so 4πr^2 = 6.0002, which should be close enough for most purposes.
Explanatory Charts, Diagrams, Photos
Think of the advantages to Nature of creating cubes vs.spheres, and vice versa;
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, Geometric and/or Trigonometric Art, Charting/Diagramming and Algebraic Formulation.
- For more art charts and graphs, you might also want to click on Category:Microsoft Excel Imagery, Category:Mathematics, Category:Spreadsheets or Category:Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page.
Video: Spheres inscribed in cubes
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Date: 03.12.2018, 03:10 / Views: 81272