Question

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

Answer 1

It may be noted that in one revolution, the bicycle covers a distance equal to the circumference of the wheel.
Total distance covered by the bicycle in 5000 revolutions = 11 km

⇒ 5000 × Circumference of the wheel = 11000 m [since 1 km = 1000 m]

Circumference of the wheel = $\left(\frac{11000}{5000}\right)$ m =2.2 m = 220 cm [since 1 m = 100 cm]

Circumference of the wheel = $\mathrm{\pi }\times \mathrm{Diameter}\mathrm{of}\mathrm{the}\mathrm{wheel}$
⇒ 220 cm = $\frac{22}{7}\times \mathrm{Diameter}\mathrm{of}\mathrm{the}\mathrm{wheel}$
⇒ Diameter of the wheel = $\left(\frac{220\times 7}{22}\right)$ cm = 70 cm
Hence, the circumference of the wheel is 220 cm and its diameter is 70 cm.