Brain Teasers
The String Around the Cylinder
A cylinder 48cm high has a circumference of 16cm. A string makes exactly 4 complete turns around the cylinder, while its two ends touch the cylinder's top and bottom (forming a spiral around the cylinder).
How long is the string in cm?
How long is the string in cm?
Hint
Pythagoras' theorem may help.Answer
80cm.Finding the length of the string is the same as finding the length of the hypotenuse of a triangle with a height of 48 cm and a base of 64 cm (16 x 4). Using Pythagoras' theorem, you get:
h^2 = 48^2 + 64^2
Solving, h = 80 cm.
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Comments
I like this one... looks ridiculously hard at first, but then something just clicks and there you go.
isn't it called pythagorean therom?
It depends. If you believe that Pythagoras himself proved the theorem, then it's called Pythagoras' Theorem. If, however, you believe it was more likely one of his disciples, then it's called the Pythagorean Theorem. As the Pythagorean Brotherhood was sworn to absolute secrecy, upon pain of death, no one will ever truly know who proved it. After all, we've taken a solemn oath.
Hey Sir: Get a life
I'm still struggling with the puzzle itself. How do you "know" 1) the triangle is a right triangle, 2) the lengths of two of the sides. I understand 48 cm is the length of one side...and you could make (with the string) another side of at least 64 cm. But, how do you know creating the 64 cm side with produce a right triangle?...because the Pythagorean Theorem requires the traingle to be a right triangle. Thanks.
You know it's a right triangle because the triangle height is made up of the can's height and the triangle base is made up of the can's circumference (four times). These two things are perpendicular to each other, and therefore form a right angle. Throw in the string as the hypotenuse, and you have a right triangle.
For an example of how to solve this problem, buy a can of Pillsbury cinnamon rolls and follow the instructions to open it... that should give you an idea how it works And if you still don't see it, at least now you have cinnamon rolls MMMMM...
I liked this one because at first it does seem to be difficult, but then as soon as I start thinking about how to solve it, the simplicity becomes apparent. Took about 20 seconds to solve.
this was a good teaser
Good teaser. I imagined rolling the cylinder out flat and then traversing it 4 times back and forth to finish at the bottom. Each travese forms a right triangle 16 by 12 giving a hypotenuse of 20. 4 x 20 = 80.
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