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?
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.
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