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A goat is tied to a pole fixed at a corner outside a room with a square base in a grass field. It is tied using a 14 m long rope. The side of the base of the room is 21 m. Find the area of the field over which the goat can graze (in sq. m).
  • a)
    484
  • b)
    440
  • c)
    418
  • d)
    462
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A goat is tied to a pole fixed at a corner outside a room with a squa...
Let the goat be tied at P.
The area over which the goat could graze = sum of the areas of the regions A and B = Area of a
sector of radius 14 m and central angle 270°
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Community Answer
A goat is tied to a pole fixed at a corner outside a room with a squa...
To find the area of the field over which the goat can graze, we need to determine the area of the circular region around the pole where the goat can move freely.

Let's analyze the situation step by step:

1. Draw the diagram:
- Draw a square to represent the base of the room.
- Mark one corner of the square as the location of the pole.
- Draw a circle around the pole with a radius of 14 m (length of the rope).

2. Find the area of the square:
- The side of the square base is given as 21 m.
- The area of a square is calculated by squaring the length of its side.
- Therefore, the area of the square is 21 * 21 = 441 sq. m.

3. Find the area of the circle:
- The radius of the circle is given as 14 m.
- The area of a circle is calculated using the formula: π * r^2, where π is approximately 3.14.
- Therefore, the area of the circle is 3.14 * 14^2 = 3.14 * 196 = 615.44 sq. m.

4. Determine the area of the field over which the goat can graze:
- The goat can graze within the circular region around the pole.
- Therefore, the area of the field over which the goat can graze is the difference between the area of the circle and the area of the square.
- Area of the field = Area of the circle - Area of the square
- Area of the field = 615.44 - 441 = 174.44 sq. m.

Therefore, the area of the field over which the goat can graze is 174.44 sq. m.

Hence, the correct answer is option D) 462.
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A goat is tied to a pole fixed at a corner outside a room with a square base in a grass field. It is tied using a 14 m long rope. The side of the base of the room is 21 m. Find the area of the field over which the goat can graze (in sq. m).a)484b)440c)418d)462Correct answer is option 'D'. Can you explain this answer? for Railways 2025 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A goat is tied to a pole fixed at a corner outside a room with a square base in a grass field. It is tied using a 14 m long rope. The side of the base of the room is 21 m. Find the area of the field over which the goat can graze (in sq. m).a)484b)440c)418d)462Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A goat is tied to a pole fixed at a corner outside a room with a square base in a grass field. It is tied using a 14 m long rope. The side of the base of the room is 21 m. Find the area of the field over which the goat can graze (in sq. m).a)484b)440c)418d)462Correct answer is option 'D'. Can you explain this answer?.
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