Final answer:
The grazing area for the cow tied to the fence post at a corner of a 300 by 100 feet field with a 50 feet rope is found by calculating the area of a quarter-circle with a radius of 50 feet, which results in 3,000π square feet.
Step-by-step explanation:
The question involves determining the grazing area available to a cow that is tethered to a fence post at one corner of a rectangular field. The rectangular field measures 300 feet by 100 feet, and the cow is tied with a 50-foot rope, which allows the cow to graze within a quarter-circle shape since it is tied at the corner of the field.
The area of a quarter-circle can be found using the formula for the area of a circle (A = πr²) and taking a quarter of it, because the cow can only graze a quarter of the full circle defined by the length of the rope.
Given that the radius (r) of the full circle that can be grazed is 50 feet, we calculate the full circle's area as π * (50²) square feet, and the actual grazing area as a quarter of that which is π * (50²) / 4 square feet. Performing the calculation, we have (3,000π square feet) as the grazing area for the cow. Therefore, the correct answer to the question is (a) 3,000π square feet.