Решебник по геометрии 9 класс Мерзляк Задание 257

\[S_{с} = \frac{5\pi}{4}\ см^{2};\ \ \ a = 75{^\circ}:\]

\[S_{с} = S_{кр} \bullet \frac{a}{360{^\circ}}\ \ \]

\[S_{кр} = \frac{360{^\circ} \bullet S_{с}}{a}\]

\[S_{кр} = \frac{360{^\circ}}{75{^\circ}} \bullet \frac{5\pi}{4} = \frac{24}{5} \bullet \frac{5\pi}{4} = 6\pi.\]

\[S_{кр} = \pi R^{2}\]

\[R = \sqrt{\frac{S_{кр}}{\pi}} = \sqrt{6}.\]

\[Ответ:\ \ \sqrt{6}\ см.\]