Question

A bicycle wheel makes 5000 revolutions in moving 11 km. Find the diameter of the wheel.

Answer 1

We have:

Total distance covered in 5000 revolutions = 11 km = 11,000 m
∴​ Distance covered in 1 revolution = $\frac{11,000}{5000}=\left(\frac{11}{5}\right)\mathrm{m}$.
Distance covered in 1 revolution = Circumference of the wheel
​$$\begin{gathered} \left(\frac{11}{5}\right)=\mathrm{\pi d} \\ \Rightarrow d=\left(\frac{11}{5\times \mathrm{\pi }}\right)=\left(\frac{11\times 7}{5\times 22}\right)\mathrm{m} \\ \Rightarrow d=\left(\frac{7}{10}\right)=0.7\mathrm{m}. \end{gathered}$$
Thus, the diameter of the wheel is 0.7 m = 70 cm.