Question

The diameter of the circle is
The diameter of a wheel of a car is 84 cm. How many revolutions will it make to
travel 264 km?​

Answer 1

Given :

• Diameter of wheel of a car = 84 cm

To find :

• Number of revolutions the car will make to travel 264 km

Knowledge required :-

→ Formula to calculate Circumference of circle :-

• Circumference = 2πr

where,

• Take π = 22/7
• r = radius

→ Formula to calculate radius :-

• Radius = Diameter ÷ 2

Unit conversion :-

• 1 cm = 0.01 m

To convert the value from cm into m divide it by 100.

• 1 km = 1000 m

To convert the value from km into m divide it by 1000.

Solution :

Firstly, convert the value of diameter of the wheel from cm into m.

⠀⠀⠀⇒ 84 cm = 84/100 = 0.84 m

Diameter of the wheel = 0.84 m

Now, we will calculate the radius of the wheel.

⠀⠀⠀⇒ Radius = Diameter ÷ 2

⠀⠀⠀⇒ Radius = 0.84 ÷ 2

⠀⠀⠀⇒ Radius = 0.42

Radius of the wheel of the car = 0.42 m

Now, we will calculate the circumference :-

⠀⠀⠀⇒ Circumference = 2πr

⠀⠀⠀⇒ Circumference = 2 × 22/7 × 0.42

⠀⠀⠀⇒ Circumference = 2 × 22/7 × 42/100

⠀⠀⠀⇒ Circumference = 2 × 22 × 6/100

⠀⠀⠀⇒ Circumference = 264/100

⠀⠀⠀⇒ Circumference = 2.64

Circumference = 2.64 m

Now, concert the circumference from m into km.

• 1 m = 1/1000 km

⠀⠀⠀⇒ 2.64 m = 2.64/1000 = 0.00264 km

Number of revolutions that the car will travel to cover 264 km = Distance ÷ Circumference

⠀⠀⠀⇒ No. of revolutions = 264 ÷ 0.00264

⠀⠀⠀⇒ No. of revolutions = 100,000

Number of revolutions that the car will travel to cover 264 km = 100,000

Answer 2

Given :

• The diameter of a wheel of a car is 84 cm.

To find :

We need to know how many revolutions will it make to travel 264 km ?

Solution :

Let , r be the radius of the wheel .

Then ,

Diameter = 84 cm

2r = 84

r = 42

Circumference of the wheel =

2πr = 264 cm = 2.64 cm

So, the wheel covers 2.64 meters in one complete revolution.

$\sf Total \: number \: of \: revolutions \: in \: covering \: 792 \: meters = \frac{792}{2.64} = 300.$

Hence, the wheel takes 300 revolutions in covering 792 meters.