Question Number 141198 by ajfour last updated on 16/May/21
Commented by ajfour last updated on 17/May/21
$${Material}\:{volume}\:{of}\:{sphere} \\ $$$${minus}\:{ellipsoid}\:{is}\:\frac{\mathrm{4}}{\mathrm{3}}\pi{c}\:. \\ $$$${Find}\:{radius}\:{of}\:{sphere}\:{R}. \\ $$$${The}\:{ellipsoid}'{s}\:{radii}\:{are} \\ $$$$\:\:\:{r}_{\mathrm{1}} =\mathrm{1}\:,\:{r}_{\mathrm{2}} =\mathrm{1},\:{r}_{\mathrm{3}} ={R}\:. \\ $$$$\:\:\left({i}\:{had}\:{meant}\:{this}\:{Sir}\right) \\ $$
Commented by mr W last updated on 16/May/21
$$\frac{\mathrm{4}\pi}{\mathrm{3}}\left({R}^{\mathrm{3}} −\mathrm{1}×\mathrm{1}×{R}\right)=\frac{\mathrm{4}\pi}{\mathrm{3}}×{R} \\ $$$$\Rightarrow{R}=\sqrt{\mathrm{2}}\:? \\ $$