Question

The diameter of a wheel is 48cm. If the car travels at an average speed of 3.5km/h.Find the number of revolutions made by wheel per min. (take pie to be 3.142)?

Answer 1

Given :

• Diameter of a wheel = 48 cm
• The average speed at which the car travels = 3.5 km/hr

To find :

• Number of revolutions made by the wheel

Knowledge Required :

Formula to calculate radius :-

• Radius = Diameter ÷ 2

Formula to calculate circumference of circle :-

• Circumference of circle = 2πr

where,

• Take π = 3.142
• r denotes radius of the circle

Solution :

Firstly, we will calculate the radius of the wheel :

⠀⠀⠀⇒ Radius = Diameter ÷ 2

⠀⠀⠀⇒ Substituting the given values :

⠀⠀⠀⇒ Radius = 48 ÷ 2

⠀⠀⠀⇒ Radius = 24

Radius of the wheel = 24 cm

Now, we will calculate the circumference of the wheel :

⠀⠀⠀⇒ Circumference of wheel = 2πr

⠀⠀⠀⇒ Substituting the given values :

⠀⠀⠀⇒ Circumference of wheel = 2 × 3.142 × 24

⠀⠀⠀⇒ Circumference of wheel = 150.816

Circumference of the wheel = 150.816 cm

∴ Distance covered by the wheel in one revolution = 150.816 cm

Convert the distance covered by the wheel in one revolution from cm into m :

As we know,

• 1 cm = 1/100 m

Divide the value by 100 to convert it from cm into m.

⠀⠀⠀⇒ Distance = 150.816 ÷ 100

⠀⠀⠀⇒ Distance = 1.50816

The total distance covered by the wheel in one revolution = 1.50816 m

We have,

• Time = 1 hour
• Speed = 3.5 km/hr

Convert the time from hour into seconds :

⠀⠀⠀⇒ Time = 1 hour = 3600 seconds

Convert the speed from km into m :

Convert the speed from km into m multiply the value by 5/18

⠀⠀⠀⇒ Speed = 3.5 km = 3.5 × 5/18

⠀⠀⠀⇒ Speed = 0.97

∴ Speed = 0.97 m/s and time = 3600 seconds

⠀⠀⠀⇒ Distance = Speed × Time

⠀⠀⠀⇒ Substituting the given values :

⠀⠀⠀⇒ Distance = 0.97 × 3600

⠀⠀⠀⇒ Distance = 3492

Total distance covered by the wheel = 3492 m

To calculate the number of revolutions made by the wheel :

Divide the total distance by circumference

⠀⠀⠀⇒ No. of revolutions = Distance ÷ Circumference

⠀⠀⠀⇒ No. of revolutions = 3492 ÷ 1.50816

⠀⠀⠀⇒ No. of revolutions = 2,315.42

After rounding off, we get :

Number of revolutions made by the wheel = 2,315