Question

The diameter of the wheel of a car is 77cm. How many revolutions will it take to travel 121m.

Answer 1

Hint: We will use the given diameter to find the radius of the wheel, as ${\text{Diameter}} = 2 \times {\text{Radius}}$. Next, find the distance that the wheel covers in one revolution by calculating the circumference of the wheel. Next, convert the distance given in centimetres and then divide the total distance by the distance covered in one revolution to find the number of revolutions covered.

Complete step-by-step answer:
We are given that the diameter of the wheel of the car is 77cm.
Then radius is the half the diameter, which is $\dfrac{{77}}{2}$ cm
The distance travelled in one revolution is the circumference of the wheel, which is given by $2\pi r$, where $r$ is the radius of the wheel.
On substituting the value of the radius and $\pi = \dfrac{{22}}{7}$, we will get,
\[2\left( {\dfrac{{22}}{7}} \right)\left( {\dfrac{{77}}{2}} \right) = 242cm\]
Thus the distance travelled in one revolution is 242cm.
But, we want to find the number of revolutions in 121m.
The total distance travelled is given in metres, but we have distance covered in cm.
Hence, we will multiply the total distance, that is 121m by 100 to convert it into cm.
$121 \times 100 = 12100cm$
Now, divide the total distance by the distance covered in one revolution to find the number of revolutions covered.
$\dfrac{{12100}}{{242}} = 50{\text{ revolutions}}$
Therefore, the wheel has to take 50 revolutions to travel 121m.

Note: Here, we have converted metres into cm, but we can also solve this question by converting the circumference of the circle into metres by dividing it by 100. We can then divide the total distance by the distance covered in one revolution to find the number of revolutions covered.