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Question Number 48196 by ajfour last updated on 20/Nov/18

Commented by ajfour last updated on 20/Nov/18

$$Findvolumeofsphereabove$$$$thetriangularplaneinterms$$$$of\mathit{a},\mathit{b},\mathit{c},and\mathit{R}.$$

Answered by mr W last updated on 20/Nov/18

$$IM=IP=IQ=r$$$$r=\frac{1}{2}\sqrt{\frac{(-a+b+c)(a-b+c)(a+b-c)}{a+b+c}}$$$$h=R-\sqrt{R^2-r^2}$$$$V=\frac{4\pi R^3}{3}-\frac{\pi h(h^2+3r^2)}{6}$$$$V=\frac{4\pi R^3}{3}-\frac{\pi (R-\sqrt{R^2-r^2})(R^2+r^2-R\sqrt{R^2-r^2})}{3}$$

Commented by ajfour last updated on 21/Nov/18

$$Thankssir,thisshallbevery$$$$helpfultome.$$

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