2023 · Q4
On a large ground, there is a straight tall vertical wall of length 28 m. A goat is tied to a point on the ground which is at the middle of the wall, using a rope. If the length of the rope is 21 m, what is the area of the region (in sq. m) around the wall that the goat can access?
general-mental-abilityquantitative-aptitude
- A847
- B851
- C693
- D654
Explanation
The goat is tied at the midpoint of the 28 m wall, so each end of the wall is 14 m away. On the near side it grazes a semicircle of radius 21 m, area (1/2) x pi x 21^2. The rope can also pass round each end of the wall, leaving 21 - 14 = 7 m free at each end, which sweeps a semicircle of radius 7 m on the far side, adding 2 x (1/2) x pi x 7^2. The total is (pi/2)(441 + 98) = (22/14) x 539 = 847 sq. m, using pi = 22/7. Hence option A.