NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 11: Area Related To Circles - Exercise 11.2
Question 6

Question. 6

In covering a distance \(s\) metres, a circular wheel of radius \(r\) metres makes \(\dfrac{s}{2\pi r}\) revolutions. Is this statement true? Why?

Answer:

true

Detailed Answer with Explanation:

Step 1: A wheel is circular. When it makes one complete turn (one revolution), the distance it moves forward is equal to the circumference of the wheel.

Step 2: The circumference of a circle is given by the formula:

\( C = 2\pi r \)

where \(r\) is the radius of the wheel (in metres, SI unit of length).

Step 3: So, in one revolution, the wheel covers a distance of \(2\pi r\) metres.

Step 4: If the wheel covers a total distance of \(s\) metres, then the number of revolutions is:

\( \text{Number of revolutions} = \dfrac{\text{Total distance}}{\text{Distance per revolution}} \)

\( = \dfrac{s}{2\pi r} \)

Step 5: This is exactly the same as given in the question. Therefore, the statement is True.

NCERT Exemplar Solutions Class 10 – Mathematics – CHAPTER 11: Area Related To Circles – Exercise 11.2 | Detailed Answers