two wheels are rotating in such a way that the rotation of t

two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. the radius of the smaller wheel is 6.5cm and the radius of the larger wheel is 19.6cm. through how many degrees will the larger wheel rotate if the smaller one rotates 223 degrees?

Solution

Let us consider,

x is the angle moved by the larger wheel.

Given that smaller wheel rotates 223 degrees.

The movement of smaller wheel : 2(6.5)*223/360

The movement of larger wheel : 2(19.6) * x/360

2(6.5)*223/360 = 2(19.6) * x/360

(6.5)*223 = (19.6)* x

x = 6.5*223/19.6

x = 73.95 degrees.