The diameter of a cycle wheel is 126 cm. A cyclist takes $$16\frac{1}{2}$$ minutes to reach the destination at a speed of 72 km/hr. How many revolutions will the wheel make during the journey?(Take $$\pi = \frac{22}{7}$$)

speed=72 km/hr=20m/s.

time=$$16\frac{1}{2}$$ minutes=990 seconds.

Diameter d of wheel=126cm.

$$radius,r=\dfrac{d}{2}$$

$$\rightarrow r=63cm$$

distance covered by wheel in one revolution=circumference of wheel

$$\rightarrow 2\pi r$$

$$\rightarrow 2\times\dfrac{22}{7}\times 63$$

$$\rightarrow 396cm$$

$$\rightarrow 3.96m$$

let it takes x rev in 990 seconds.

distance covered x xrevolutions=$$speed\times time$$ 

$$\rightarrow 3.96x=20\times 990$$

$$\rightarrow x=\dfrac{20\times 990}{3.96}$$

$$\rightarrow x=5000$$