What must be the radius of a wheel if an arc 24pi cm long subtends an angle of 72 at the Centre?

Text Solution

Solution : Let the required radius be r cm. Then, <br> `l = 22 cm` and `theta = (72 xx pi/180)^(c )= ((2pi)/5)^(c )`. <br> Now, `theta = l/r rArr r = l/theta= (22 xx 5/(2pi)) cm` <br> `= (22 xx 5/2 xx 7/22) cm` <br> `= 35/2 cm = 17.5 cm`. <br> Hence, the radius of the circle is `17.5` cm. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/RSA_MATH_XI_C14_S01_004_S01.png" width="80%">.