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To make a cylindrical tube, a rectangular piece of paper 31.4 centimet

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To make a cylindrical tube, a rectangular piece of paper 31.4 centimet  [#permalink]

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New post 07 Dec 2017, 04:37
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To make a cylindrical tube, a rectangular piece of paper 31.4 centimeters wide and 50 centimeters long was rolled lengthwise and the two longer edges were taped together. If there was no overlap where the taping occurred, approximately what was the radius, in centimeters, of the tube?

(A) 5
(B) 7
(C) 10
(D) 15
(E) 25

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To make a cylindrical tube, a rectangular piece of paper 31.4 centimet  [#permalink]

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New post 07 Dec 2017, 09:41
Bunuel wrote:
To make a cylindrical tube, a rectangular piece of paper 31.4 centimeters wide and 50 centimeters long was rolled lengthwise and the two longer edges were taped together. If there was no overlap where the taping occurred, approximately what was the radius, in centimeters, of the tube?

(A) 5
(B) 7
(C) 10
(D) 15
(E) 25

Attachment:
cc.png
cc.png [ 6.81 KiB | Viewed 309 times ]

Nice question. Once the paper has been rolled the long way (see diagram), the short edge of what was a rectangle becomes the circumference of a circular edge of the tube on the top and on the bottom.

The length of the rectangle's short side, 31.4, is a big hint about what to do.
The two edges of the tube are circles.
Each circle's circumference, it's "length," is still 31.4 centimeters. But that length must involve \(π\) and a radius.

Radius of the tube, in centimeters, derived from circumference:

\(2πr = 31.4\)

\(2r = \frac{31.4}{π}\)

\(2r = \frac{31.4}{3.14}\)
\(2r = 10\)
\(r \approx{5}\)

Answer A

The "approximately" comes from rounding π to 3.14
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To make a cylindrical tube, a rectangular piece of paper 31.4 centimet &nbs [#permalink] 07 Dec 2017, 09:41
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