SOLUTION: A roll of news paper of length 7000m and thickness 0.022cm is rolled into a solid cylinder. Then it's radius is what?

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Question 1100341: A roll of news paper of length 7000m and thickness 0.022cm is rolled into a solid cylinder. Then it's radius is what?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

Let x be the width in meters of the roll of newspaper.

We need to use consistent units; so call the thickness of the newspaper 0.00022m.

Spread out into a rectangular sheet, the newspaper is a very thin rectangular solid with length 7000, width x, and thickness 0.00022. The volume is then 1.54x cubic meters.

When rolled into a cylinder, the volume will be the same.

The volume of a cylinder is (pi)*(radius squared)*(height); the height of the cylinder is the width of the newspaper. So

1.54x+=+%28pi%29%28r%5E2%29x
r%5E2+=+1.54%2F%28pi%29+=+0.49 (approximately... 0.490197....)
r+=+sqrt%280.49%29+=+0.7

The radius of the roll of newspaper is approximately 0.7m.