Question

A bicycle wheel is $1mand26cm$ in diameter. Calculate

(i) The distance travelled in one rotation of the wheel.

(ii) The number of rotations of the wheel that needs to cover$1.98km.$

Answer 1

Step 1: Finding the radius of the wheel:

Given diameter is $1mand26cm$

$$\begin{gathered} diameter=100+26(1m=100cm) \\ =126cm. \end{gathered}$$

radius$=\frac{diameter}{2}$

$$\begin{gathered} =\frac{126}{2} \\ =63cm. \end{gathered}$$

Step 2: Finding the distance travelled by one rotation:

Distance travelled by one rotation$=2\mathrm{\pi r}\mathrm{where}\mathrm{r}\mathrm{is}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{circle}.$

$$\begin{gathered} =2\times \frac{22}{7}\times 63 \\ =2\times 22\times 9 \\ =396cm \end{gathered}$$

$$\begin{gathered} 396cm=300+96cm \\ =3\times 100+96cm(1m=100cm) \\ =3mand96cm \end{gathered}$$

Distance travelled by one rotation is $3mand96cm.$

Step 3:Finding the number of rotations to cover $1.98km.$

$$\begin{gathered} 1.98km\text{can be written as}198000cm(1km=100000cm \\ 1.98km=1.98\times 100000 \\ =198000cm) \end{gathered}$$

number of rotations $=\frac{totaldis\tan ceof1.98km}{dis\tan cetravelledbyonerotation}$

$$\begin{gathered} =\frac{198000}{396} \\ =500 \end{gathered}$$

Therefore, $500$rotation is needed in order to cover the distance of $1.98km.$

Hence, the distance travelled by one rotation is $3mand96cm$and $500$rotation is needed in order to cover the distance of $1.98km.$