Category: Geometry

Question Number 183628 by a.lgnaoui last updated on 27/Dec/22 $${surface}\:{du}\:{rectangle}? \\ $$ Commented by a.lgnaoui last updated on 27/Dec/22 Commented by Frix last updated on…

Question Number 52539 by ajfour last updated on 09/Jan/19 Answered by mr W last updated on 09/Jan/19 $${p}=\frac{\sqrt{\left[\left({b}+{c}\right)^{\mathrm{2}} −{a}^{\mathrm{2}} \right]\left[{a}^{\mathrm{2}} −\left({b}−{c}\right)^{\mathrm{2}} \right]}}{\mathrm{2}{a}} \\ $$$${r}=\frac{\sqrt{\left[\left({b}+{c}\right)^{\mathrm{2}} −{a}^{\mathrm{2}}…

Question Number 118069 by Lordose last updated on 15/Oct/20 $$\left.\mathrm{1}\left..\right)\mathrm{i}\right)\:\mathrm{A}\:\mathrm{right}\:\mathrm{circular}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{circumscribed} \\ $$$$\mathrm{about}\:\mathrm{a}\:\mathrm{sphere}\:\mathrm{of}\:\mathrm{radius}\left(\boldsymbol{\mathrm{r}}\right).\:\:\mathrm{If}\:\boldsymbol{\mathrm{d}}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{distance}\:\mathrm{from}\:\mathrm{the}\:\mathrm{center}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sphere} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone},\:\mathrm{show}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone},\boldsymbol{\mathrm{V}}=\frac{\boldsymbol{\pi\mathrm{r}}^{\mathrm{2}} \left(\boldsymbol{\mathrm{r}}+\boldsymbol{\mathrm{d}}\right)^{\mathrm{2}} }{\mathrm{3}\left(\boldsymbol{\mathrm{d}}−\boldsymbol{\mathrm{r}}\right)}. \\ $$$$\left.\mathrm{ii}\right) \\ $$$$\boldsymbol{\mathrm{F}}\mathrm{ind}\:\mathrm{the}\:\mathrm{vertical}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{when} \\…

Question Number 183558 by Acem last updated on 27/Dec/22 Commented by Acem last updated on 27/Dec/22 $$\:{The}\:{inlet}\:{segment}\:\bot\:{Hypotenuse} \\ $$ Answered by HeferH last updated on…

Question Number 52468 by mr W last updated on 08/Jan/19 Commented by mr W last updated on 08/Jan/19 $${No}\:{friction}. \\ $$$${Find}\:\theta=? \\ $$ Commented by…