Overview
To determine the area of the square field where the horse cannot graze, we need to analyze the grazing area based on the length of the rope and the dimensions of the field.
Field Dimensions
- The side length of the square field is 30 m.
- The area of the square field = side × side = 30 m × 30 m = 900 m².
Rope Length and Grazing Area
- The length of the rope is 40 m, allowing the horse to graze in a circular area.
- The area the horse can graze = π × (radius)² = π × (40 m)² ≈ 5026.55 m².
Interaction Between Grazing Area and Field
- The horse is tied at the center of the field, meaning the grazing area extends beyond the boundaries of the square field.
- The square field has corners, and since the rope is longer than the side of the field, the horse can graze outside the field in certain areas.
Area Where Horse Cannot Graze
- The grazing area overlaps with the corners of the square field.
- The area where the horse cannot graze is the area of the square field minus the area the horse can graze that lies within the square.
Calculating Non-Grazable Area
1. The total area of the square field = 900 m².
2. The area the horse can graze is larger than the square field, thus:
- Area of grazing outside the field = grazing area - area of the field.
- Since the horse can graze 5026.55 m² but only 900 m² is available, the horse cannot graze in the corners of the field.
3. Therefore, the non-grazable area = Area of the square field = 900 m².
Conclusion
- The area of the field where the horse cannot graze is essentially the corners of the square field, but since the horse can reach the field's center, the non-grazable area remains 900 m².