Ex.11.3 Q16 Perimeter and Area - NCERT Maths Class 7

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Question

How many times a wheel of radius \(28 \rm\,cm\) must rotate to go \(352 \rm\,m\)? \(\begin{align}\left( {{\text{Take }}\pi = \frac{{22}}{7}} \right)\end{align}\)

Text Solution

What is known?

A wheel of \(28 \rm\,cm\).

What is unknown?

Number of times the given wheel must rotate to go \(352 \rm\,m\).

Reasoning:

The distance covered by the wheel in one revolution is equal to the circumference of the wheel. Now, to find out the number of times wheel should rotate, divide the total distance covered by the circumference of the wheel. 

Steps:

Radius of wheel \(=\) \(28 \rm\,cm\)

Circumference of wheel

\[\begin{align} &= 2\pi r \\ &= 2 \times \frac{{22}}{7} \times 28\\ &= 2 \times 22 \times 4\\ &= 176\;\rm\,cm\end{align}\]

Total distance \(=\) \(352 \rm\,m\) \(= 35200 \rm\,cm\)

No of times wheel should rotate

\[\begin{align} &= \frac{\text{Total distance covered by wheel}}{\text{Circumference of the wheel}}\\&= \frac{{35200}}{{176}}\\&= 200\end{align}\]

Therefore, wheel must rotate \(200\) times to go \(352 \rm\,m\).