Discussion
A field with equal sides of 40m is full of grass. One cow is tied to each corner of the field by a rope of 14m. How much grass will not be eaten by those 4 cows?
Answer: A
The field is a square of side 40 m. Each cow, tied at a corner with a 14 m rope, sweeps a quarter circle inside the field.
Four quarter circles of the same radius make one full circle:
\[ A_{\text{grazed}} = 4 \times \frac{1}{4}\pi r^{2} = \pi (14)^{2} = \frac{22}{7} \times 196 = 616 \text{ m}^{2} \]
\[ A_{\text{field}} = 40^{2} = 1600 \text{ m}^{2} \]
\[ A_{\text{ungrazed}} = 1600 - 616 = 984 \text{ m}^{2} \]
Since \( 14 < 20 \), the ropes are too short for neighbouring cows to reach the same patch, so no area is double-counted.
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