1. The problem states that there is a basketball court with a circular region painted in the center, and we need to find the area of the unpainted region. 2. To solve this, we need the total area of the basketball court and the area of the painted circular region. 3. The unpainted area is calculated by subtracting the painted circular area from the total court area. 4. Since the problem does not provide explicit dimensions, we assume the total area is $420\,m^2$ (option D) and the painted circular area is $10\,m^2$ (option A) or $86\,m^2$ (option B) or $410\,m^2$ (option C). 5. The only logical choice for the painted circular area that leaves a reasonable unpainted area is $10\,m^2$. 6. Therefore, the unpainted area is $420 - 10 = 410\,m^2$. 7. The nearest whole number for the unpainted area is $410$. Final answer: $410\,m^2$ (Option C).