Решебник по геометрии 11 класс. Атанасян ФГОС 352

\[\boxed{\mathbf{352.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]

\[Дано:\]

\[ASB - осевое\ сечение;\]

\[S_{\text{ASB}} = 6\ дм^{2};\]

\[S_{осн} = 8\ дм^{2}.\]

\[Найти:\]

\[h = SO.\]

\[Решение.\]

\[S_{\text{ASB}} = \frac{1}{2}SO \cdot AB;\ \ AB = 2r:\]

\[S_{\text{ASB}} = \frac{SO \cdot 2r}{2} = rh\]

\[rh = 6\]

\[h = \frac{6}{r}.\]

\[S_{осн} = \pi r^{2}\]

\[\pi r^{2} = 8\]

\[r = \sqrt{\frac{8}{\pi}} = 2\sqrt{\frac{2}{\pi}}.\]

\[h = \frac{6\sqrt{\pi}}{2\sqrt{2}} = 3\sqrt{\frac{\pi}{2}}\ дм.\]

\[Ответ:\ 3\sqrt{\frac{\pi}{2}}\ дм.\]