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I'm trying to create a sphere around one known dimension - the radius of what would be a spherical cap. The spherical cap would have a volume equal to one-third the volume of the whole sphere.

radius of spherical cap, r=692.820323

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    Can you use integrals? – graydad Jan 15 '15 at 22:36
  • I am aware that this would be the key, however, I myself am ignorant with executing integrals. If someone can walk me through it, that would be great! – user208187 Jan 15 '15 at 23:07
  • I am rusty in multivariable calculus, but I think I can figure something out. First, please clarify: The $r$ you have is the radius of the sphere? Or $r$ is the radius of the cap, if you are measuring from the flat/bottom part of the cap's center to an edge? – graydad Jan 15 '15 at 23:08
  • My r is the radius of the cap. – user208187 Jan 15 '15 at 23:12

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Hint: integrate along the radius of the sphere (the area).