Question

If the radius of a wheel is \( \dfrac{35}{44} \) metre, then the distance covered in \(2\) revolutions is:

• A. \(10\ \text{m}\)
• B. \(35\ \text{m}\)
• C. \(22\ \text{m}\)
• D. \(40\ \text{m}\)

Hint:

Distance in \(n\) revolutions \(= n \times 2\pi r\). For clean numbers, use \(\pi=\frac{22}{7}\) when \(r\) has factors \(7\) or \(11\).

Answer 1

The Correct Option is A

Step 1: Use the circumference formula.
Distance in one revolution \(= 2\pi r\). For \(2\) revolutions, distance \(= 4\pi r\).
Step 2: Substitute \( r=\dfrac{35}{44} \) m and \( \pi=\dfrac{22}{7} \).
\[ \text{Distance} = 4\pi r = 4 \times \frac{22}{7} \times \frac{35}{44} = \frac{140}{44}\times \frac{22}{7} = \frac{35}{11}\times \frac{22}{7} = \frac{770}{77} = 10\ \text{m}. \]
Step 3: Conclude.
Hence, the distance covered in \(2\) revolutions is \(10\) metres.