Find the diameter of a wheel that makes 113 revolutions to go 2 km 26 decameters.

### Concept & Formula The diameter of a wheel is related to the distance covered and the number of revolutions: $$\text{Total Distance} = n \times (\pi d)$$ $$d = \frac{\text{Total Distance}}{n \times \pi}$$ Unit conversion: $$1\text{ kilometer (km)} = 1000\text{ meters (m)}$$ $$1\text{ decameter (dam)} = 10\text{ meters (m)}$$ ### Step-by-Step Solution * **Convert total distance to meters:** $$\text{Total Distance} = 2\text{ km} + 26\text{ dam} = (2 \times 1000) + (26 \times 10) = 2000 + 260 = 2260\text{ m}$$ * **Given:** * Revolutions ($n$) = $113$ * **Distance covered in 1 revolution (Circumference):** $$C = \frac{2260}{113} = 20\text{ m}$$ * **Calculate diameter ($d$):** $$\pi d = 20$$ $$\frac{22}{7} \times d = 20$$ $$d = \frac{20 \times 7}{22} = \frac{140}{22} = \frac{70}{11}\text{ m}$$ * **Convert to mixed fraction:** $$\frac{70}{11} = 6\frac{4}{11}\text{ m}$$ ### Exam Strategy & Shortcut Observe that $2260 = 113 \times 20$, so $C = 20\text{ m}$. $$d = \frac{20 \times 7}{22} = \frac{70}{11} = 6\frac{4}{11}\text{ m}$$ ### Common Pitfall Confusing decameter ($1\text{ dam} = 10\text{ m}$) with decimeter ($1\text{ dm} = 0.1\text{ m}$). ### Final Answer Therefore, the correct answer is **6\frac{4}{11}\text{ m}**.