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Question-141198




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 (4/3)πc .  Find radius of sphere R.  The ellipsoid′s radii are     r_1 =1 , r_2 =1, r_3 =R .    (i had meant this Sir)
$${Material}\:{volume}\:{of}\:{sphere} \\ $$$${minus}\:{ellipsoid}\:{is}\:\frac{\mathrm{4}}{\mathrm{3}}\pi{c}\:. \\ $$$${Find}\:{radius}\:{of}\:{sphere}\:{R}. \\ $$$${The}\:{ellipsoid}'{s}\:{radii}\:{are} \\ $$$$\:\:\:{r}_{\mathrm{1}} =\mathrm{1}\:,\:{r}_{\mathrm{2}} =\mathrm{1},\:{r}_{\mathrm{3}} ={R}\:. \\ $$$$\:\:\left({i}\:{had}\:{meant}\:{this}\:{Sir}\right) \\ $$
Commented by mr W last updated on 16/May/21
((4π)/3)(R^3 −1×1×R)=((4π)/3)×R  ⇒R=(√2) ?
$$\frac{\mathrm{4}\pi}{\mathrm{3}}\left({R}^{\mathrm{3}} −\mathrm{1}×\mathrm{1}×{R}\right)=\frac{\mathrm{4}\pi}{\mathrm{3}}×{R} \\ $$$$\Rightarrow{R}=\sqrt{\mathrm{2}}\:? \\ $$

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