# 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?

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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