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Formula for Volume of a Sphereor

Formula for Volume of a Sphereor

Formula for Volume of a Sphere

In this article we make a simplified model for calculating the volume of a sphere. We make a circle, calculate the perimeter, find the radius, and then multiply them together. Then we use formulas to find the volume of a sphere based on those dimensions.

Use

If you're willing to accept that you know the volume of a cone is 1/3 that of the cylinder with the same base and height, you can use Cavalieri, comparing a hemisphere to a cylinder with an inscribed cone, to get the volume of the sphere. This diagram (from Wikipedia) illustrates the construction: look here

$\begingroup$ I dont want to criticize the validity of the result, but frankly the use of higher mathematics as a means to prove lower mathematics seems irrational and circular in reasoning. To respect the natural conceptual evolution of mathematics is, to me, the foremost way to proving math and explaining it to students. $\endgroup$ How you refer to the different dimensions does not change the calculation: you may, for example, use 'depth' instead of 'height'. The important thing is that the three dimensions are multiplied together. You can multiply in which-ever order you like as it won't change the answer (see our page on multiplication for more). (Source: www.skillsyouneed.com)

 

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