Question

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when car is traveling at a speed of 66 km per hour.
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Answer 1

Given : The Speed of the Car is 66 km per hour

Given : The Diameter of the Car wheel = 80 cm

⇒ Radius of the Car wheel = Half of the Diameter = 40 cm

As the Question asks about the Revolutions of each wheel in 10 minutes and the Diameter of the Car wheel is in Centimeters, Lets change the Units of Speed of the Car into Centimeters per Minute

We know that : One Kilometer = 100000 centimeters and 1 hour contains 60 Minutes.

$\mathsf{\implies Speed\;of\;the\;Car = (66 \times \frac{100000}{60}) = 110000\;cm\;per\;min}$

It means Car covers a Distance of 110000 centimeters in One Minute.

It means Car covers a Distance of 1100000 centimeters in 10 Minutes

In order to Solve this Problem, We need to Realize the fact that : After Each Revolution of the Wheel, It covers a Distance which is Equal to the Circumference of the Wheel.

⇒ After One Revolution of Each Wheel, The Car covers a Distance which is Equal to the Circumference of the Wheel

We know that : Circumference of a Circle is given by : 2π × Radius

⇒ Circumference of the Wheel = (2π × 40) = 251.33 cm

Let the Number of Revolutions made by the Wheel in those 10 minutes be : N

Now, We can realize that : The Product of the Number of Revolutions made by the Wheel in those 10 Minutes and The Circumference of the Wheel should be Equal to the Distance traveled by the Car in those 10 Minutes

$\mathsf{\implies N \times 251.33 = 1100000}$

$\mathsf{\implies N = (\frac{1100000}{251.33})\;Revolutions}$

$\mathsf{\implies N = 4377\;Revolutions\;(approx)}$