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The Creeper on the Tree

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1. A creeper plant is climbing up and around a cylindrical tree trunk in a helical manner. The tree trunk has a height of 300 inches and a circumference of 32 inches.

If the creeper covers a vertical distance of 60 inches in one complete twist around the tree trunk, what is the total length of the creeper?
Answer: 340

Solution:

puzzle : creeper on the tree To make visualization easy, it is convenient to conceptually open out the bark of the tree trunk and flatten it. The cylindrical surface will then be a rectangle (as illustrated in the figure alongside for 4 twists of the creeper).

It may be noted that:
Width of the rectangle = Circumference of the cylinder = 32 inches.

Height of the rectangle = Vertical distance on the cylinder = 60 inches (in one twist).

Using the Pythagorean Theorem for a right-angled triangle,

Length of the hypotenuse = (322 + 602) 1/2 = 68 inches.

Now, the number of twists the creeper makes around the tree trunk is 5 (= 300 / 60).

If the length of the creeper (as given by the hypotenuse) is 68 inches in one twist, then the total length of the creeper in 5 twists is 340 inches.

Food for thought:

Is the total length of the creeper in the above calculation the actual length or the minimum length?

  Try the Quiz :     Puzzles & Brain Teasers : The Creeper on the Tree


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