what is the formula to calculate major arc length , ??

You don't need to rely on a formula Its just another thing to remember.
Lets work it out. How many radians in a full circle?
 
Harry_the_cat said:
You don't need to rely on a formula Its just another thing to remember.
Lets work it out. How many radians in a full circle?
Click to expand...
I have just solved it , I got 87.9 cm , the but it would be nice if you give me your wayou of doing in without formula.
 
When a central angle (call it theta) is measured in radians, it subtends an arc length equal to the radian measure times the radius. Subtract that minor arc length from the circumference, to get the major arc length:

2 * Pi * r - theta * r

or

r * (2 * Pi - theta)

?
 
The full circle is 2*Pi radians.
The minor arc is subtended by 1.4 radians.
So the minor arc is 1.4/(2*Pi) of the circumference, ie 1.4/(2*Pi) * 2*Pi*r =1.4 *r.
(The 2*Pi cancels ... that's why the arc length = radian measure times radius, as Otis said.)
The major arc length can be found by subtracting the minor arc from the circumference.
 
dev644 said:
... without formula.
Click to expand...
Another way to work it out: Remember the definition of a radian.

1 radian is defined as the angle (theta) which subtends an arc length equal to the radius. Therefore, in a unit circle, the arc length always equals theta. So, when theta is 1.4 radians in a unit circle, the arc length subtended is 1.4 units.

When we enlarge the unit circle by a factor, both the radius and the arc length enlarge by the same factor because a circle and its parts increase proportionately. That is, if we increase the unit radius by a factor of 18, the arc length (1.4 units) also increases by a factor of 18.

Therefore, your angle COD subtends an arc length of 18*1.4 (radius times radians).

Hopefully, you can remember the circumference formula.

;)
 
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