1-A-right-circular-cone-is-circumscribed-about-a-sphere-of-radius-r-If-d-is-the-distance-from-the-center-of-the-sphere-to-the-vertex-of-the-cone-show-that-the-volume-of-the-cone-V-r-2-r-d-

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Question Number 118104 by Lordose last updated on 15/Oct/20

$$1.)$$$$\mathrm{A}\mathrm{right}\mathrm{circular}\mathrm{cone}\mathrm{is}\mathrm{circumscribed}$$$$\mathrm{about}\mathrm{a}\mathrm{sphere}\mathrm{of}\mathrm{radius}\left(\mathbf{r}\right).\mathrm{If}\mathbf{d}\mathrm{is}\mathrm{the}$$$$\mathrm{distance}\mathrm{from}\mathrm{the}\mathrm{center}\mathrm{of}\mathrm{the}\mathrm{sphere}$$$$\mathrm{to}\mathrm{the}\mathrm{vertex}\mathrm{of}\mathrm{the}\mathrm{cone},\mathrm{show}\mathrm{that}\mathrm{the}$$$$\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{cone},\mathbf{V}=\frac{\mathit{\pi }{\mathbf{r}}^2{(\mathbf{r}+\mathbf{d})}^2}{3(\mathbf{d}-\mathbf{r})}.$$$$2.)$$$$\mathbf{F}\mathrm{ind}\mathrm{the}\mathrm{vertical}\mathrm{angle}\mathrm{of}\mathrm{the}\mathrm{cone}\mathrm{when}$$$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{volume}\mathrm{is}\mathrm{minimum}.$$

Commented by 1549442205PVT last updated on 15/Oct/20

$$\mathrm{This}\mathrm{is}\mathrm{repeated}\mathrm{question}\mathrm{Q}118069$$

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