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A can is in the shape of a right circular cylinder. The circumference of the base of the can is 12 inches, and the height of the can is 5 inches. A spiral strip is painted on the can in such a way that it winds around the can exactly once as it reaches from the bottom of the can to the top. It reaches the top of the can directly above the spot where it left the bottom. What is the length in inches of the stripe?

Thanks!

 Nov 27, 2019

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A can is in the shape of a right circular cylinder. The circumference of the base of the can is 12 inches, and the height of the can is 5 inches. A spiral strip is painted on the can in such a way that it winds around the can exactly once as it reaches from the bottom of the can to the top. It reaches the top of the can directly above the spot where it left the bottom. What is the length in inches of the stripe?     

 

Do a mental experiment.  Cut the cylinder at one spot along its length, and uncurl it and lay it flat.  You now have a rectangle, with width equal to the circumference of the cylinder (12 inches), and length equal to the length of the cylinder (5 inches).  Paint the strip from one corner of the rectangle to the opposite corner.  Now just use Pythagoras' Theorem to determine that the length of that strip is 13 inches

 

PS - I actually did this, with an empty toilet paper roller.  Of course the specific dimensions were different, but the principle is the same.  

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 Nov 27, 2019
 #1
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I'm getting sqrt(601).

 Nov 27, 2019
 #2
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+1
Best Answer

 

A can is in the shape of a right circular cylinder. The circumference of the base of the can is 12 inches, and the height of the can is 5 inches. A spiral strip is painted on the can in such a way that it winds around the can exactly once as it reaches from the bottom of the can to the top. It reaches the top of the can directly above the spot where it left the bottom. What is the length in inches of the stripe?     

 

Do a mental experiment.  Cut the cylinder at one spot along its length, and uncurl it and lay it flat.  You now have a rectangle, with width equal to the circumference of the cylinder (12 inches), and length equal to the length of the cylinder (5 inches).  Paint the strip from one corner of the rectangle to the opposite corner.  Now just use Pythagoras' Theorem to determine that the length of that strip is 13 inches

 

PS - I actually did this, with an empty toilet paper roller.  Of course the specific dimensions were different, but the principle is the same.  

.

Guest Nov 27, 2019

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