# The wheels of a car are of diameter 80 cm each.

Question:

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

Solution:

Diameter of the wheel of the car = 80 cm Then,

the radius of the wheel of the car

= 40 cm = 0.4 cm

Distance travelled by the car when the wheel of the car completes one revolution

$=2 \pi \times(0.4) \mathrm{m}=\frac{\mathbf{4} \pi}{\mathbf{5}} \mathbf{m}$

Let us suppose the wheel of the car completes n revolutions in 10 minutes when travelling at the speed of 66 km per hour. Then distance travelled by making n complete revolution of the wheel in 10 minutes

$=\left(\frac{4 \pi}{5} \times \mathbf{n}\right) \mathrm{m}$

Also, distance travelled in 60 minutes

$=66 \mathrm{~km}=66 \times 1000 \mathrm{~m}$

Then the distance travelled in 10 minutes

$=\frac{\mathbf{6 6} \times \mathbf{1 0 0 0}}{\mathbf{C D}} \times 10 \mathrm{~m}=11000 \mathrm{~m}$

Therefore, we have $\frac{\mathbf{4} \pi}{\mathbf{5}} \times \mathbf{n}=11000$

$(\because$ Distance travelled in 10 minutes is same)

$\Rightarrow \frac{4}{5} \times \frac{22}{7} \times n=11000$

$\Rightarrow \mathrm{n}=\frac{\mathbf{1 1 0 0 0} \times \mathbf{5} \times \mathbf{7}}{\mathbf{4} \times \mathbf{2 2}}=125 \times 35=4375$

Hence, the number of complete revolutions made by the wheel in 10 minutes is 4375.