Calculate the length of the arc if its radian measure a and the radius R

Calculate the length of the arc if its radian measure a and the radius R of the circle containing it are known: a) a = 2, R = 1 cm; b) a = 0.1 and R = m;

To begin with, let’s draw two arcs, in the first we denote the angle as 2 rad, and the radius as 1 cm, and in the second arc we denote the angle as 0.1 radians, and the radius as m.

Since the length of the arc is sought by the formula C = 2 * pi * R / a, where pi is 3.14 rad, R is the radius, and this is the angle in degrees.

Let’s convert radians to degrees: 2 rad = 114.6, and 0.1 rad is 0.003.

Then the length of the first arc is: (2 * 3.14 * 1) / 114.6 = 0.06 cm.

Then the length of the second circle is: (0.1 * 3.14 * m) / 0.003 = 104.7 * m.