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

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Question

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.

Reasoning:

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

Steps:

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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