Question

The wheels of a car make 2500 revolutions in covering a distance of 4.95 km. Find the diameter of a wheel.

Answer 1

Distance = 4.95 km = $4.95\times 1000\times 100\mathrm{cm}$
∴ Distance covered by the wheel in 1 revolution $=\frac{\mathrm{Total}\mathrm{distance}\mathrm{covered}}{\mathrm{Number}\mathrm{of}\mathrm{revolutions}}$

$$\begin{gathered} =\frac{4.95\times 1000\times 100}{2500} \\ =198\mathrm{cm} \end{gathered}$$

Now,
Circumference of the wheel = 198 cm
$$\begin{gathered} \Rightarrow 2\pi r=198 \\ \Rightarrow 2\times \frac{22}{7}\times r=198 \\ \Rightarrow r=\frac{198\times 7}{44} \\ \Rightarrow r=31.5\mathrm{cm} \end{gathered}$$

∴ Diameter of the wheel = 2r
= 2(31.5)
= 63 cm