# A wheel of a car has a radius 21 cm. If it is rotating at 800 RPM, what is the speed of the car?

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The radius of the wheel is 21 cm. When the wheel rotates once, the distance covered by the car is 2*pi*21.

As the wheel rotates at 800 RPM, it covers a distance equal to 2*pi*21*800 cm per minute.

The distance covered in one hour is 2*pi*21*800*60/100 m

=> 20160*pi m

=> 20.16*pi km

=> 63.33 km (approximately)

**The required speed of the car is 20.16*pi or 63.33 km/hr**.

The radius r of the wheel of the car = r = 21cm.

So in one rotation of the wheel, the distance the car moves = 2pi*r = 2pi*21/100 meter.

So the distance moved by the car in 800 RPM = 2pi*21*800/100 meter.

So the speed of the car per minute = 2pi*21*800/100 = 1055.575m.

So the speed of the car per hour = 1055.576*60/1000 km

= 63.33 kilo meter/ hour.

The formula of speed when knowing the number of rotations per minute is:

s = pi*D*n/1000

D = diameter of the wheel = 2*210 = 420 mm

pi = 3.14 approx

n = 800 rpm

Now, we'll introduce the data into the formula above:

s = 3.14*420*800/1000

We'll simplify and we'll get:

s = 3.14*42*8

s = 1055.04*60 minutes

s = 63302.4

s = 63.3 Km/hour