perplexus.info :: Shapes : Two way tube.

Two way tube. (Posted on 2009-06-15)

A rectangular piece of paper can be rolled into a tube in two different ways. (Edges should not overlap.)

When it is rolled up the long way the volume enclosed is 2500/π cm³.
When is is rolled up the short way the volume enclosed is 3125/π cm³.

Find the area of the piece of paper.

Submitted by Jer

Rating: 1.5000 (2 votes)

Solution: (Hide)

500 cm²
Call the dimensions x and y.
It is simple enough to show the volumes are x²y/(4π) and xy²/(4π)
This gives x²y=10000 and xy²=12500
Solving this system x=20 and y=25
xy = 20*25 = 500

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-07-21 01:50:02
general solution	Daniel	2009-06-16 02:05:15
solution	Daniel	2009-06-15 19:05:41

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