Question

0.15. The diameter of the wheel of a vehicle is 1.4 m. How many rotations will the wheel complete
in travelling a distance of 2.2 km?
Solution:​

Answer 1

Given :

• The diameter of the wheel of a vehicle is 1.4 m.

To find :

• How many rotations will the wheel completein travelling a distance of 2.2 km ?

Solution :

$\\\large{\blue{\underline{\boxed{\bf{\blue{Circumference\:of\:circle=1\: rotation}}}}}}$

• Diameter of wheel = 1.4 m
• Radius of wheel = 1.4/2 = 0.7m

$\\\large{\underline{\bf{\red{Circumference\:of\:circle=2\pi r}}}}$

$\implies\sf 2\pi{r}$

$\implies\sf 2\pi{r}$

$\implies\sf 2\times\dfrac{22}{7}\times{r}$

$\implies\sf 2\times\dfrac{22}{7}\times{0.7}$

$\implies\sf 2\times{22}\times{0.1}$

$\implies\sf {4.4m}$

${\underline{\bf{\purple{Circumference\:of\:circle=4.4m=1\:rotation}}}}$

The rotations will the wheel complete in travelling a distance of 2.2 km

$\\\small\bigstar\:\large\tt{\pink{1kilometer = 1000m}}\:\small\bigstar$

• 2.2km = 2.2 × 1000 = 2200 m

$\\\large{\underline{\sf{\green{Number\:of\:rotations}}}}$

$\implies\sf \cancel\dfrac{2200}{4.4}$

$\implies\sf 500$

500 rotations will the wheel complete in travelling a distance of 2.2km

_________________________________

Answer 2

Answer:

Given :-

• The diameter of the wheel of a vehicle is 1.4 m.

To Find :-

• How many rotations will the wheel complete in traveling a distance of 2.2 km.

Formula Used :-

${\red{\boxed{\large{\bold{Circumference\: of\: Circle\: =\: 2{\pi}r}}}}}$

where,

• r = Radius

Solution :-

First, we have to find the radius,

As, we know that,

★ $\sf Radius =\: \dfrac{Diameter}{2}$ ★

Then,

↦ $\sf Radius =\: \dfrac{1.4}{2}$

➦ $\sf\bold{\pink{Radius =\: 0.7\: m}}$

Now, we have to find circumference of a circle,

Given :

• Radius = 0.7 m

According to the question by using the formula we get,

⇒ $\sf Circumference\: =\: 2 \times \dfrac{22}{7} \times 0.7$

⇒ $\sf Circumference\: =\: \dfrac{44}{7} \times$

⇒ $\sf Circumference =\: \dfrac{44}{\cancel{7}} \times \dfrac{\cancel{7}}{10}$

⇒ $\sf Circumference =\: \dfrac{44}{10}$

➠ $\sf\bold{\purple{Circumference =\: 4.4\: m}}$

Hence, the circumference of a circle is 4.4 m.

Now, we have to find how many rotations will the wheel complete in traveling a distance of 2.2 m,

As we know that,

✧ 1 kilometres = 1000 m ✧

Then, 2.2 km = 2.2 × 1000

$\implies$ 2200 m

Hence, number of rotation will be,

↪ $\sf \dfrac{2200}{4.4}$

↪ $\sf \dfrac{2200 \times 10}{44}$

↪ $\sf \dfrac{\cancel{22000}}{\cancel{44}}$

➤ $\sf\bold{\green{500}}$

$\therefore$ 500 rotations will the wheel complete in traveling a distance of 2.2 m.