A cow is tethered at the centre of a circular field with a rope 14 feet long. If the cow can graze 100 square feet of grass per day, approximately how many days will it take to graze the entire field? (Use π ≈ 22/7.)

Introduction / Context:
This question involves calculating the area of a circle and then relating that area to a constant rate of grazing. It is a practical example of how circular area, measured using π and radius, can be converted into a time duration when the rate of work or consumption is known, in this case grazing per day.

Given Data / Assumptions:

• Length of rope (radius of field) r = 14 feet
• Grazing rate = 100 square feet per day
• Shape of field = full circle that the cow can reach
• Use π ≈ 22/7 for calculations

Concept / Approach:
The cow can reach all points within a circle of radius 14 feet. First, compute the total grazable area of this circle using the formula Area = π * r^2. Then divide the total area by the daily grazing rate to find the approximate number of days required. Because the answer is not an integer, it is presented to two decimal places for practical approximation.

Step-by-Step Solution:
Area of circular field A = π * r^2 Using π = 22/7 and r = 14: A = (22/7) * 14 * 14 Simplify: 14 * 14 = 196 A = (22/7) * 196 = 22 * 28 = 616 square feet Daily grazing rate = 100 square feet per day Time required (in days) = Total area / rate = 616 / 100 = 6.16 days

Verification / Alternative check:
You can check by multiplying 6.16 * 100 = 616 square feet, which matches the circle area. If you estimated roughly, you might say a little more than 6 days, and 6.16 days provides a precise decimal approximation.

Why Other Options Are Wrong:
7.16 days and 8.16 days: These imply total grazed area of 716 or 816 square feet, which exceeds the actual field area. 5.16 days: This would cover only about 516 square feet, which is less than the full field. 10.16 days: Greatly overestimates the time and implies grazing far more than the available area.

Common Pitfalls:
Using diameter 28 instead of radius 14 in the area formula. Forgetting to square the radius when computing area. Rounding π or the final result too roughly and losing accuracy.

Final Answer:
The cow will take approximately 6.16 days to graze the entire field