The diameter of a cycle wheel is 70 cm. A cyclist takes 30 hours to reach a destination at the speed of 22 km/hr. How many revolutions will the wheel make during this journey?

### Concept & Formula The total number of revolutions ($n$) made by a wheel is given by dividing the total distance traveled by the circumference of the wheel. $$\text{Circumference } (C) = \pi d$$ $$n = \frac{\text{Total Distance}}{\text{Circumference}}$$ ### Step-by-Step Solution * **Given:** * Diameter ($d$) = $70\text{ cm} = \frac{70}{100}\text{ m} = 0.7\text{ m}$ * Speed = $22\text{ km/hr}$ * Time = $30\text{ hours}$ * **Calculate total distance covered:** $$\text{Total Distance} = \text{Speed} \times \text{Time} = 22 \times 30 = 660\text{ km}$$ $$\text{Total Distance in meters} = 660 \times 1000 = 660000\text{ m}$$ * **Calculate circumference of the wheel:** $$C = \frac{22}{7} \times 0.7 = 2.2\text{ m}$$ * **Calculate the number of revolutions ($n$):** $$n = \frac{660000}{2.2} = 300000 = 3\text{ lakh}$$ ### Exam Strategy & Shortcut Work in consistent units directly: $$n = \frac{22 \times 30 \times 10^5\text{ cm}}{\frac{22}{7} \times 70\text{ cm}} = \frac{660 \times 10^5}{220} = 3 \times 10^5 = 3\text{ lakh}$$ ### Common Pitfall Mismatched units: confusing kilometers, meters, centimeters, and Indian numbering terms (lakh $= 10^5$). ### Final Answer Therefore, the correct answer is **3 lakh**.