Question

Diameter of a wheel is $3$ m. The wheel revolves $28$ times in a minute to cover the distance of $5.280$ km the wheel will take how much time? $(\pi =\frac{22}{7})$

• A. $10$ minutes
• B. $20$ minutes
• C. $30$ minutes
• D. $40$ minutes

Answer 1

Answer: (B)

$20$ minutes

It is given that the diameter of the wheel is $d=3$ m, therefore, the radius of the wheel is:

$r=\frac{d}{2}=\frac{3}{2}=1.5$ m

We know that the circumference of the circle is $2\pi r$ where $r$ is the radius of the circle.

The distance covered by the wheel in one revolution is as follows:

$2\pi r=2\times \frac{22}{7}\times 1.5=\frac{2\times 22\times 1.5}{7}=\frac{66}{7}$ m

The distance covered by the wheel in one minute will be:

$28\times \frac{66}{7}=4\times 66=264$ m

Now,

$5.280$ km$=5.280\times 1000=5280$ m

Thus, time taken to cover $5.280$ km is:

$\frac{5280}{264}=20$ min

Hence, time taken to cover $5.280$ km is $20$ minutes.