Title: सूर्य में छेद (Sun with a Cut)
Content: Answer to an Indian Game Problem (English)
Assumption:
The title likely refers to a 几何 (geometry) problem involving a circular "sun" shape with a sector cut out. The task is to calculate the remaining area and perimeter after the cut.
Sample Problem & Solution:
Problem:
A circular sun (radius = 6 cm) has a sector cut out with a central angle of 60°. Find:
Remaining area.
Remaining perimeter (including the cut edges).
Solution:
Radius (R): 6 cm
Original Area:
[
\text{Area} = \pi R^2 = \pi \times 6^2 = 36\pi , \text{cm}^2
]
Cut Sector Area (60°):
[
\text{Sector Area} = \frac{60}{360} \times \pi R^2 = \frac{1}{6} \times 36\pi = 6\pi , \text{cm}^2
]
Remaining Area:
[
36\pi - 6\pi = 30\pi , \text{cm}^2 \quad (\approx 94.25 , \text{cm}^2)
]
Original Perimeter:
[
2\pi R = 12\pi , \text{cm}
]
Cut Sector Arc Length:
[
\text{Arc Length} = \frac{60}{360} \times 2\pi R = 2\pi , \text{cm}
]
Remaining Perimeter:
[
\text{Remaining Arc} + 2 \times \text{Radius} = (12\pi - 2\pi) + 2 \times 6 = 10\pi + 12 , \text{cm} \quad (\approx 51.4 , \text{cm})
]
Key Steps:
Area Calculation: Subtract the cut sector’s area from the total.
Perimeter Calculation: Subtract the arc length of the cut and add twice the radius (for the straight edges of the cut).
If the Problem is Different:
If the game involves a strategy/puzzle (e.g., rearranging pieces or solving a riddle), provide additional details like:
Game rules.
Visual description of the cut.
Target objective (e.g., maximize/minimize area).
Let me know for a tailored solution! 🌞✨
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