Q1. [4]
A stable owner has four horses. He usually tie these horses with 7 m long rope to pegs at each corner of a square shaped grass field of 20 m length, to graze in his farm. But tying with rope sometimes results in injuries to his horses, so he decided to build fence around the area so that each horse can graze.
Based on the above, answer the following questions :
- (i) Find the area of the square shaped grass field. [1]
- (ii) Find the area of the total field in which these horses can graze. [2]
- (iii) What is area of the field that is left ungrazed, if the length of the rope of each horse is 7 cm ? [1]
Previously asked in CBSE board exam
2024 30/3/1 Q36
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding stimulus
Model Answer
(i) Area of square field = side² = 20 × 20 = 400 m²
(ii) Each horse is tied at a corner of a square, so each grazes a quarter-circle of radius 7 m.
Area grazed by one horse = $\frac{1}{4}\pi r^2 = \frac{1}{4} \times \frac{22}{7} \times 7 \times 7 = \frac{1}{4} \times 154 = 38.5 \text{ m}^2$
Total area grazed by 4 horses = 4 × 38.5 = 154 m²
(iii) Area left ungrazed = Area of field − Area grazed
= 400 − 154 = 246 m²
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Explanation
- Each corner of a square has an interior angle of 90°, so each horse grazes a sector of angle 90° (i.e., a quarter-circle) with radius = rope length = 7 m.
- Four such quarter-circles together make one full circle: 4 × (¼πr²) = πr².
- Sub-question (iii) uses the same rope length (7 m — the "cm" in the question is a typo in the original; treat it as 7 m, consistent with the passage). Examiners expect students to catch this consistency.
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