 Hello and welcome to the session. In this session we will discuss a question which says that given a central angle of 2 by 3, find the length of its intercepted arc in a circle of radius 10 inches rounded to the nearest length. Now before starting the solution of this question we should know how it is out and that is the radian measure theta of the central angle of a circle is the length of the intercepted arc s divided by radius r of the circle. Now here theta is the central angle subtended by the arc s and theta is equal to a pole radius circle which is equal to s a pole r is equal to s which is equal to r theta. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now here we have given a circle of radius 10 inches. The central angle is 2 by 3 length of intercepted Here we have given radian measure of angle. If we were given the degree measure then we would have first converted it into radian measure and then we would have proceeded. Now here as we are given radian measure of central angle so let us proceed with the solution. First of all let us make a diagram for this question. Now here we have drawn a circle with center o and radius op is equal to 10 inches. Now we know by angle length the central angle subtended by arc s that is theta is equal to 2 but is equal to 10 inches that is radius of the circle is equal to 10 inches. Here we know that length is equal to r theta is equal to now r and theta is s is equal to 10 into 2 pi by 3. Now we know that pi is equal to 3.14 or 22 by 7. Now here let us put pi is equal to 3.14 so this implies 10 into 2 into 3.14 upon 3 on solving we get s is equal to 20.933. Now rounding us to the nearest 10th we have length 20.9 inches approximately. So this is the solution of the given question and that is all for this session. Hope you all have enjoyed the session.