How to express volume of a sphere as a sum of infinitesimally thick discs?I want to express the volume of a sphere with a radius r as an integral that adds up each infinitesimally thick disc within the volume. So I have d V = A ( x ) d x, where A(x) is the area of the disc that is at coordinate x. I'm having trouble finding this function in terms of r. Remember, r is the radius of the sphere. At x = 0 , A = π r 2 , and at x = r , A = 0. The bounds of the integral should be -r to r I believe. But what is A(x)?

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How to express volume of a sphere as a sum of infinitesimally thick discs?I want to express the volume of a sphere with a radius r as an integral that adds up each infinitesimally thick disc within the volume. So I have   d  V  =  A  (  x  )  d  x, where A(x) is the area of the disc that is at coordinate x. I&#039;m having trouble finding this function in terms of r. Remember, r is the radius of the sphere. At   x  =  0  ,  A  =      π        r          2      , and at   x  =  r  ,  A  =  0. The bounds of the integral should be -r to r I believe. But what is A(x)?

Jordyn Valdez · Accepted Answer

Explanation:                    V        =        ∑        π        (                  r                      2                          −                  x                      2                          )        δ        x        =        π                  ∫                      −            r                                r                          (                  r                      2                          −                  x                      2                          )        d        x            A little integral calculus and you will recover the well known result.       V    S    =      4    3    π      r    3

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