A dog is tied to a tree by a long nylon cord. If the dog runs from the

Question

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

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

farful · Answer

Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.

The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.

pi*r = 30. Round pi = 3, then r = 10.

Chord is about 10 feet long.

singhabhijeet · Answer

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 times. This means that dog ran in semi - circle or 180 degree sector is create.

We know that length of arc = ( \frac{central angle}{360}  ) * 2* PI * r 
therefore, =  \frac{180}{360} * 2* PI * r = 30

=> PI * r = 30 
3.142 * r = 30

r= 10 (approx)

sophieA · Answer

Hi guys!
Sorry, but I still don't get it. Can anyone explain this to me please?

Because I understand it as a dog runs half of the circle, in my mind a cord should be the same length as a semicircle. How come a cord is shorter than a semicircle aka equals to radius? I get how to solve it, I just don't understand the logic. Thank you very much for your help!

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ScottTargetTestPrep · Answer

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

TestPrepUnlimited · Answer

sophieA 
Think of a simple pendulum with a ring at the end of a string. When you are waving the pendulum the ring follows a circular arc and the string has the equivalent function of the rope in this question.

rsrighosh · Answer

i thought dog ran along the diameter from North to South.
But i do not understand that why we should take it as semicircle and not along diameter. Where is this mentioned in the question??

RajdeepGM · Answer

The question asks: If half the circumference of the circle is 30, what is the radius.

So 2* pi* r = 60
ie r = 10 (approx)

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A dog is tied to a tree by a long nylon cord. If the dog runs from the

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