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?

Hint:

To calculate the number of wheel revolutions, first find the circumference of the wheel, convert the speed to the appropriate unit, and then divide the distance traveled by the circumference.

Answer 1

Step 1: Find the circumference of the wheel.
The diameter of the wheel is given as 80 cm, so the radius is: \[ r = \frac{80}{2} = 40 \, \text{cm} \] The circumference \( C \) of the wheel is given by: \[ C = 2\pi r = 2 \times \frac{22}{7} \times 40 = \frac{1760}{7} = 251.43 \, \text{cm} \]
Step 2: Convert the speed of the car to cm/min.
The speed of the car is given as 66 km/h. To convert this to cm/min: \[ 66 \, \text{km/h} = 66 \times 1000 \, \text{m/h} = 66000 \, \text{cm/h} \] Since there are 60 minutes in an hour: \[ \text{Speed in cm/min} = \frac{66000}{60} = 1100 \, \text{cm/min} \]
Step 3: Calculate the distance traveled in 10 minutes.
In 10 minutes, the car will travel: \[ \text{Distance traveled} = 1100 \times 10 = 11000 \, \text{cm} \]
Step 4: Calculate the number of revolutions.
To find the number of revolutions, divide the distance traveled by the circumference of the wheel: \[ \text{Number of revolutions} = \frac{\text{Distance traveled}}{\text{Circumference}} = \frac{11000}{251.43} \approx 43.75 \] So, each wheel makes approximately **44 complete revolutions** in 10 minutes.