Ex.12.1 Q4 Areas Related to Circles Solution - NCERT Maths Class 10

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The wheels of a car are of diameter \(80\, \rm{cm}\) each. How many complete revolutions does each wheel make in \(10\) minutes when the car is traveling at a speed of \(66\, \rm{km}\) per hour?

Text Solution

What is known?

Diameter of the wheel of the car and the speed of the car.

What is unknown?

Revolutions made by each wheel.


Distance travelled by the wheel in one revolution is nothing but the circumference of the wheel itself.


Diameter of the wheel of the car \(= 80\,\rm{cm}\)

Radius \((r)\) of the wheel of the car \(= 40\,\rm{cm}\)

Distance travelled in \(1\) revolution \(=\) Circumference of wheel

Circumference of wheel

\[\begin{align}&= 2\pi \,{ r}\\& = 2\pi \left( {{\text{40}}} \right)\\&= 80\pi\, \rm{cm}\end{align}\]

Speed of car\(= 66\, \text{km/hour}\)

\[\begin{align}&= \frac{{66 \times {\text{ }}100000}}{{60}}\,{\text{cm/}}\,{\text{min}}\\&= 110000 {\text{ cm/min}}\end{align}\]

Distance travelled by the car in \(10\) minutes

\[\begin{align}&= {\text{ }}110000{\text{ }} \times {\text{ }}10{\text{ }}\\&= {\text{ }}1100000{\text{ cm}}\end{align}\]

Let the number of revolutions of the wheel of the car be \(n\)

\(\rm{n} \times\)Distance travelled in\(1\) revolution \(=\)Distance travelled in \(10\) minutes

\[\begin{align}\\\rm{n} \times 80\pi &= 1100000\\{\text{n}} &= \frac{{1100000 \times 7}}{{80 \times 22}}\\ &= \frac{{35000}}{8}\\&= 4375\end{align}\]

Therefore, each wheel of the car will make \(4375\) revolutions.

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