Is it true that the distance travelled by a circular wheel of diameter \(d\) cm in one revolution is \(2\pi d\) cm? Why?
Step 1: When a circular wheel makes one complete revolution, the distance it covers is equal to the circumference of the wheel.
Step 2: The formula for circumference is:
\( C = 2\pi r \) or \( C = \pi d \)
where \(r\) = radius of the wheel and \(d\) = diameter of the wheel.
Step 3: In SI units, if the diameter is given as \(d\) cm, we must first convert to metres (since SI unit of length is metre):
\( d\,\text{cm} = \dfrac{d}{100}\,\text{m} \).
Step 4: Substituting into the circumference formula:
\( C = \pi d \) (in cm) or \( C = \pi \times \dfrac{d}{100} \) m (in SI).
Step 5: The statement says distance = \(2\pi d\). But the correct formula is \(\pi d\).
Conclusion: Therefore, the given statement is False.