Question Number 14073 by tawa tawa last updated on 27/May/17
Commented by ajfour last updated on 27/May/17
Commented by ajfour last updated on 27/May/17
Commented by ajfour last updated on 27/May/17
$$\boldsymbol{{Q}}\left(\mathrm{1}\right). \\ $$$${A}=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{2}{x}\right){y} \\ $$$${y}={r}\mathrm{sec}\:\theta+{r} \\ $$$$\:\:={r}\left(\mathrm{1}+\mathrm{sec}\:\theta\right) \\ $$$${x}={y}\mathrm{cot}\:\theta \\ $$$$\:\:={r}\left(\mathrm{1}+\mathrm{sec}\:\theta\right)\mathrm{cot}\:\theta \\ $$$${A}={xy}={r}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{sec}\:^{\mathrm{2}} \theta\right)\mathrm{cot}\:\theta\:. \\ $$
Commented by tawa tawa last updated on 27/May/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$
Answered by ajfour last updated on 27/May/17
$$\boldsymbol{{Q}}\left(\mathrm{2}\right). \\ $$$${h}={r}\mathrm{cosec}\:\theta+{r} \\ $$$${h}={r}\left(\mathrm{1}+\mathrm{cosec}\:\theta\right) \\ $$$${R}={h}\mathrm{tan}\:\theta\:={r}\left(\mathrm{1}+\mathrm{cosec}\:\theta\right)\mathrm{tan}\:\theta \\ $$$${V}=\frac{\mathrm{1}}{\mathrm{3}}\pi{R}^{\mathrm{2}} {h} \\ $$$${V}\:=\frac{\mathrm{1}}{\mathrm{3}}{r}^{\mathrm{3}} \left(\mathrm{1}+\mathrm{cosec}\:\theta\right)^{\mathrm{3}} \mathrm{tan}\:^{\mathrm{2}} \theta\:. \\ $$
Commented by tawa tawa last updated on 27/May/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$