Geometry Questions

Question Number 102241 by ajfour last updated on 07/Jul/20

Commented by ajfour last updated on 07/Jul/20

$${If}\:{the}\:{solid}\:{cylinder}\:{and}\:{sphere}\:{have} \\$$$${the}\:{same}\:{density}\:,\:{find}\:{maximum} \\$$$${R}\:{such}\:{that}\:{cylinder}\:{doesn}'{t}\:{topple}. \\$$$${center}\:{of}\:{sphere}\:{is}\:{at}\:{a}\:{level}\:{of}\:{half} \\$$$${the}\:{cylinder}\:{height}\:{h}.\:{radius}\:{of} \\$$$${cylinder}\:{is}\:{r}. \\$$

Commented by mr W last updated on 07/Jul/20

$${i}\:{think}\:{it}\:{doesn}'{t}\:{matter}\:{at}\:{which} \\$$$${level}\:{the}\:{center}\:{of}\:{the}\:{sphere}\:{is}. \\$$

Commented by ajfour last updated on 07/Jul/20

$${true},\:{i}\:{understand}. \\$$

Answered by mr W last updated on 07/Jul/20

$${W}_{{C}} =\pi{r}^{\mathrm{2}} {h}\rho{g} \\$$$${W}_{{S}} =\frac{\mathrm{4}\pi{R}^{\mathrm{3}} }{\mathrm{3}}\rho{g} \\$$$${W}_{{C}} {r}\geqslant{W}_{{S}} {R} \\$$$$\pi{r}^{\mathrm{2}} {h}\rho{gr}\geqslant\frac{\mathrm{4}\pi{R}^{\mathrm{3}} }{\mathrm{3}}\rho{gR} \\$$$${R}\leqslant{r}\sqrt[{\mathrm{4}}]{\frac{\mathrm{3}{h}}{\mathrm{4}{r}}} \\$$

Commented by ajfour last updated on 07/Jul/20

$${Great}\:{Sir},\:{well}\:{presented},\:{give}\:{me} \\$$$${a}\:{hint}\:{sir},\:{what}\:{questions}\:{would}\:{you} \\$$$${like}\:{from}\:{me}?\:{I}\:{am}\:{not}\:{in}\:{good} \\$$$${health},\:{its}\:{been}\:{months}\:{but}\:{these} \\$$$${days}\:{progress}\:{is}\:{good},\:{and}\:{it}\:{feels} \\$$$${great}\:{discussing}\:{with}\:{you},\:\:{but}\:{in} \\$$$${some}\:{questions}\:{i}\:{lack}\:{the}\:{patience} \\$$$${that}\:{you}\:{put}\:{in},\:{say}\:{the}\:{minimum} \\$$$${velocity}\:{question},\:{i}\:{dint}\:{review}\:{it}.. \\$$

Commented by mr W last updated on 07/Jul/20

$${sorry}\:{to}\:{know}\:{that}\:{you}\:{are}\:{not}\:{in} \\$$$${good}\:{health}\:{sir}!\:{i}\:{hope}\:{sincerely}\:{that} \\$$$${you}\:{will}\:{get}\:{well}\:{as}\:{soon}\:{as}\:{possible}. \\$$$${in}\:{fact}\:{i}\:{find}\:{all}\:{questions}\:{from}\:{you} \\$$$${creative}\:{and}\:{interesting}.\:{it}'{s}\:{a}\:{big} \\$$$${pleasure}\:{to}\:{discuss}\:{with}\:{you}\:{and}\:{to} \\$$$${see}\:{how}\:{you}\:{solve}\:{the}\:{problems}.\:{but} \\$$$${at}\:{the}\:{moment}\:{i}\:{don}'{t}\:{wish}\:{that}\:{you} \\$$$${give}\:{or}\:{solve}\:{any}\:{questions},\:{but}\:{that} \\$$$${you}\:{take}\:{more}\:{care}\:{of}\:{your}\:{health}! \\$$

Commented by ajfour last updated on 07/Jul/20

$${thanks}\:{for}\:{all}\:{your}\:{concern}\:{Sir},\:{but} \\$$$${i}\:{am}\:{comfortable}\:{now}\:{with}\:{posting} \\$$$${and}\:{answering}\:{few}\:{questions}\:{at}\:{the} \\$$$${forum}. \\$$

Commented by PRITHWISH SEN 2 last updated on 07/Jul/20

$$\mathrm{get}\:\mathrm{well}\:\mathrm{soon}\:\mathrm{sir}. \\$$

Commented by \$@y@m last updated on 08/Jul/20

https://tse2.mm.bing.net/th?id=OGC.035af8113ed0cbc479f25d449b737284&pid=Api&rurl=https%3a%2f%2fmedia.giphy.com%2fmedia%2fl2JJEZL5S5BAsFY5y%2fgiphy.gif&ehk=FsBG2ECL%2bvUZA84z1bKZjhzZWE%2fTO7f8leFAoQpAE9s%3d

Answered by 1549442205 last updated on 08/Jul/20

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