Question

The diameter of a wheel of a bus Is $90\mathrm{cm}$ which makes $315$ revolutions per minute. Determine its speed In kilometres per hour. [ Use $\pi =\frac{22}{7}$]

Answer 1

Step 1. Determine the Circumference of the wheel.

The diameter of a wheel of a bus Is $90\mathrm{cm}$.

Use the formula $C=\pi d$ to find the circumference:

$\begin{array}{rcl}C& =& \pi \times 90\mathrm{cm}\\ & \Rightarrow & \mathrm{C}=\frac{22}{7}\times 90\mathrm{cm}\\ & \Rightarrow & \mathrm{C}=\frac{1980}{7}\mathrm{cm}\end{array}$

So, the circumference is $\begin{array}{rcl}& & \frac{1980}{7}\mathrm{cm}\end{array}$.

Step 2. Determine the distance covered by the wheel.

The wheel makes $315$revolutions in a minute.

Find the total distance covered in $315$ revolutions:

$315\times \frac{1980}{7}\mathrm{cm}=89100\mathrm{cm}$

Determine the speed:

The wheel covers $89100\mathrm{cm}$ in 1 minute.

So, the speed of the wheel is $89100\frac{\mathrm{cm}}{\min }$.

Convert the speed to kilometre per hour:

$$\begin{gathered} 89100\frac{\mathrm{cm}}{\min }=89100\frac{\mathrm{cm}}{\min }\times 60\frac{\min }{\mathrm{hr}}\times \frac{1}{100000}\frac{\mathrm{km}}{\mathrm{cm}} \\ \Rightarrow 89100\frac{\mathrm{cm}}{\min }=\frac{89100\times 60}{100000}\frac{\mathrm{km}}{\mathrm{hr}} \\ \Rightarrow 89100\frac{\mathrm{cm}}{\min }=53.46\frac{\mathrm{km}}{\mathrm{hr}} \end{gathered}$$

So, the speed of the wheel is $53.46\frac{\mathrm{km}}{\mathrm{hr}}$.