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A-sphere-of-radius-r-contains-a-cyllinder-of-possible-largest-volume-Determine-the-volume-of-the-cyllinder-




Question Number 5334 by Rasheed Soomro last updated on 08/May/16
A sphere of radius r  contains a cyllinder of possible  largest volume.Determine the volume of the cyllinder.
$$\mathrm{A}\:\boldsymbol{\mathrm{sphere}}\:\mathrm{of}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{r}}\:\:\mathrm{contains}\:\mathrm{a}\:\boldsymbol{\mathrm{cyllinder}}\:\mathrm{of}\:\mathrm{possible} \\ $$$$\mathrm{largest}\:\boldsymbol{\mathrm{volume}}.\boldsymbol{\mathrm{D}}\mathrm{etermine}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\boldsymbol{\mathrm{cyllinder}}. \\ $$
Commented by Rasheed Soomro last updated on 10/May/16
I believe that the cyllinder of possible largest volume   inside a sphere has equal diameter and height.
$$\mathrm{I}\:\mathrm{believe}\:\mathrm{that}\:\mathrm{the}\:\mathrm{cyllinder}\:\mathrm{of}\:\mathrm{possible}\:\mathrm{largest}\:\mathrm{volume}\: \\ $$$$\mathrm{inside}\:\mathrm{a}\:\mathrm{sphere}\:\mathrm{has}\:\mathrm{equal}\:\mathrm{diameter}\:\mathrm{and}\:\mathrm{height}. \\ $$

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