Решебник по геометрии 8 класс Атанасян ФГОС Задание 1214

\[\boxed{\mathbf{1214.ОК\ ГДЗ - домашка\ на\ 5}}\]

\[Дано:\]

\[цилиндр;\]

\[\textbf{а)}\ r = 2\sqrt{2}\ см;h = 3\ см:\]

\[V = \pi r^{2}h = \pi \bullet \left( 2\sqrt{2} \right)^{2} \bullet 3 =\]

\[= \pi \bullet 8 \bullet 3 = 24\pi\ см^{2}.\]

\[\textbf{б)}\ V = 120\ см^{3};h = 3,6\ см:\]

\[V = \pi r^{2}h\]

\[120 = \pi r^{2} \bullet 3,6\]

\[r^{2} = \frac{120}{3,6\pi} = \frac{1200}{36\pi} = \frac{100}{3\pi}\]

\[r = \frac{10}{\sqrt{3\pi}}\ см.\]

\[\textbf{в)}\ r = h;V = 8\pi\ см^{3}:\]

\[V = \pi r^{2}h\]

\[\pi h^{2} = V\]

\[h^{3} = \frac{8\pi}{\pi} = 8\]

\[h = 2\ см.\]

\[Ответ:а)\ 24\pi\ см^{3};б)\frac{10}{\sqrt{3\pi}}\ см;\]

\[\textbf{в)}\ 2\ см.\]