Объём шара равен: \(V = \frac{4}{3}\pi {R^3},\) где R – радиус шара. Тогда:
\(\frac{4}{3}\pi {R^3} = \frac{4}{3}\pi {R_1}^3 + \frac{4}{3}\pi {R_2}^3 + \frac{4}{3}\pi {R_3}^3\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{R^3} = {6^3} + {8^3} + {10^3}\,\,\,\,\,\, \Leftrightarrow \)
\( \Leftrightarrow \,\,\,\,\,\,{R^3} = {2^3}\left( {{3^3} + {4^3} + {5^3}} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{R^3} = {2^3} \cdot {6^3}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{R^3} = {12^3}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,R = 12.\)
Ответ: 12.