Question

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

Answer 1

Step 1: Interpret the given data.
Diameter of each wheel of the car is $80cm.$
Speed of the car is $66km/hr.$

Step 2: Finding the number of complete revolutions.
The number of complete revolutions each wheel makes in $10$ minutes.

Distance travelled by the car in $1hr=66km/hr$
Distance travelled by the car in $10\text{mins}=\frac{66}{60}\times 10$
$11km$
$=11\times 1000\times 100cm$
Now,
Diameter of the wheel is $80cm$.
Radius of the wheel $=\frac{\text{diameter}}{2}$
$=\frac{80}{2}cm$
$=40cm$

Circumference of wheel of the car$=2\pi r$
$=2\times \frac{22}{7}\times 40$
$=\frac{1760}{7}cm$
So distance travelled by the car when the wheels make one complete rotation $=\frac{1760}{7}cm$
Number of revolutions made by the wheels in $10$ minutes.

$=\frac{\text{distance cannoct by the car is 10 minutes}}{\text{distance travelled by the car when its wheels complete are revalution}}$

$=\frac{11\times 1000\times 100}{\frac{1760}{7}}$

$=\frac{11\times 1000\times 100\times 7}{1760}$
$=4375$ revolutions.
\Hence, Number of revolution made by the wheels of the car in $10$ min $=4375$.