# The radius of a wheel is 0.25 m.

Question:

The radius of a wheel is 0.25 m. The number of revolutions it will make to travel a distance of 11 km will be

(a) 2800

(b) 4000

(c) 5500

(d) 7000

Solution:

We have given the radius of the wheel that is 0.25 cm.

We know that distance covered by the wheel in one revolution $=\frac{\text { Distance moved }}{\text { Number of revolutions }}$.

Distance covered by the wheel in one revolution is equal to the circumference of the wheel.

$2 \pi r=\frac{\text { Distance moved }}{\text { Number of revolutions }}$......(1)

Distance moved is given as 11 km so we will first convert it to m.

$\therefore 11 \mathrm{~km}=11000 \mathrm{~m}$

Now we will substitute the values in equation (1),

$2 \times \pi \times 0.25=\frac{11000}{\text { Number of revolutions }}$

Now we will substitute $\pi=\frac{22}{7}$.

$2 \times \frac{22}{7} \times 0.25=\frac{11000}{\text { Number of revolutions }}$

Simplifying equation (1) we get,

Number of revolutions $=\frac{11000 \times 7}{2 \times 22 \times 0.25}$

$\therefore$ Number of revolutions $=\frac{11000 \times 7}{22 \times 0.5}$

$\therefore$ Number of revolutions $=\frac{1000 \times 7}{2 \times 0.5}$

$\therefore$ Number of revolutions $=\frac{7000}{1}$

$\therefore$ Number of revolutions $=7000$

Therefore, it will make 7000 revolutions to travel a distance of $11 \mathrm{~km}$.

Hence, the correct answer is option $(d)$.