A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side

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A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord, in feet?

A) 30
B) 25
C) 15
D) 10
E) 5

Answer: D

Source: Princeton Review

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The dog runs from the North side to the South side of the tree (semi-circle) with the cord to its full length at all times.
The dog runs approximately 30 feet.
Target question: what was the approximate length of the nylon cord, in feet?
$$Circumference\ of\ a\ fall\ circle=2\pi r$$
$$Circumference\ of\ a\ semi\ circle=\frac{2\pi r}{2}=\pi r$$
Since the dog covered 30 feet
$$\pi r=30;\ \ Take\ \pi\ to\ be\ 3.142$$
So, 3.142r = 30
$$r=\frac{30}{3.142}=9.55\approx10feet$$
Therefore, option D is the correct answer

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Gmat_mission wrote: ↑
Thu Sep 24, 2020 2:35 am
A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord, in feet?

A) 30
B) 25
C) 15
D) 10
E) 5

Answer: D

Solution:


Since the nylon cord was extended to its full length at all times, the dog followed a path which is a semicircular arc with a radius equal to the length of the cord. We are given that the dog ran approximately 30 feet, so the circumference of the complete circle is 60 feet.

Since circumference = 𝜋 * d, the diameter of the circle is 60/𝜋, which is approximately 19. Thus, the radius (which equals the length of the cord) is approximately 19/2 = 9.5. Among the answer choices, 10 is the closest one.

Answer: D

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