The wheel of a motor cycle is of radius 35 cm.

Given, radius of wheel, r = 35 cm

Circumference of the wheel $=2 \pi r$

$=2 \times \frac{22}{7} \times 35$

$=220 \mathrm{~cm}$

But speed of the wheel $=66 \mathrm{kmh}^{-1}=\frac{66 \times 1000}{60} \mathrm{~m} / \mathrm{min}$

$=1100 \times 100 \mathrm{cmmin}^{-1}$

$=110000 \mathrm{cmmin}^{-1}$

$\therefore$ Number of revolutions in $1 \mathrm{~min}=\frac{110000}{220}=500$ revolution

Hence, required number of revolutions per minute is 500.