# The length if an arc traversed by minute hand of a watch 1 cm long after 15 minute as?

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Ben
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Mar 8, 2018

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This should be the radius times the angular displacement in radians, written as

#### Explanation:

It can be defined that Arc length = Angle(rad)*Radius. Radians are dimensionless, so we don't need to do any conversion!

We know the radius to be 1 cm, but we don't know the angle explicitly.

What we do know is that a full revolution of a minute hand means the hand rotated

Therefore, we can use a basic ratio to figure out the number of radians 15 minutes gives

Now that we know the angular displacement, we can calculate the arclength:

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