the radius of a wheel rolling on the ground is 80 cm. if the wheel rotates through an angle of 60 degrees. how many cm does it move

If the radius is 80cm the circumference is 2pi*80cm.

If the wheel rotates by 60° then a fraction 60/360 (= 1/6) of the circumference moves over the ground.  So the distance moved is 2pi*80/6cm

$${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{80}}}{{\mathtt{6}}}} = {\mathtt{83.775\: \!804\: \!095\: \!727\: \!819\: \!7}}$$

or approximately 84cm