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Definition of linear dimension?
For example, on a number line (which is one dimensional object), we measure the distance of two points in units. For example, the distance between 2 and 4 is 2 units. Any nth side of a polygon, can be measured by using linear units, such as cm, in., ft, km, etc. The circumference of a circle, the length of an arc, also are measured by linear units. A unit that is used to measure the distance between two points, is called linear dimension.
Why is the answer for arc length in units and not in square units?
Because it is still length. It is measured along a curve (arc), rather than a straight line. It can be found by multiplying the arc angle (in radians) by the radius. So a complete circle has an angle of 2*pi radians. Multiply this by the radius and you have 2*pi*radius, which is the circumference of a circle (measured in units, not square units).
How do you find the length of a minor arc of a circle?
If the radius of the circle is r units and the angle subtended by the arc at the centre is x radians, then the length of the arc is r*x units. If you are still working with angles measured in degrees, then the answer is r*pi*y/180 where the angle is y degrees. If r and x (or y) are not available, or cannot be deduced, then you cannot find the length of the arc.
How do you find the diameter when you only have the arc measure and length?
Suppose the angle of the arc is x radians and the length of the arc is a units. Then, if the radius of the circle is r units, a = rx or r = a/x So d = 2a/x units of length.
What is the length of the arc formed by central angle 2x?
If the angle is 2x radians then the length of the arc is 2x*r units where the radius of curvature is r units. If you measure the angle in degrees, then the length of the arc is pi*x*r/90 units.
