Question

The radius of a circular wheel is 42cm, then find the distance travelled by it 200 revolutions in m.

Answer 1

Hint: We will first find the distance travelled in one revolution by calculating the circumference of the wheel using the formula, $2\pi r$, where $r$ is the radius and $\pi = \dfrac{{22}}{7}$. Then, multiply the distance travelled in 1 revolution by 200 to find the distance travelled. At, last divide it by 100 to find the distance in metres.

Complete step-by-step answer:
We are given that the radius of the circular wheel is 42m.
We have to find the distance travelled in 200 revolutions.
Now, we know that the distance travelled in one revolution can be calculated by finding the circumference of the circle.
Also, the circumference of the circle is $2\pi r$, where $r$ is the radius of the circle.
On substituting the value of $r = 42$ and $\pi = \dfrac{{22}}{7}$, we will get the distance travelled in one revolution.
$2\left( {\dfrac{{22}}{7}} \right)\left( {42} \right) = 264cm$
But, we have to find the distance travelled in 200 revolutions.
Therefore, we will multiply the distance travelled in 1 revolution by 200 to find the total distance.
$264 \times 200 = 52,800cm$
Also, we have to find the distance in metres. Therefore, divide the above distance by 100 as 100cm makes 1m.
$\dfrac{{52,800}}{{100}}m = 528m$
Hence, the total distance covered by wheel in 200 revolutions is 528m.

Note: Circumference is the length of the boundary of the circle. When a wheel revolves, the distance covered is equal to the circumference of the circle. Also, students should know the formula of circumference of the circle, which is $2\pi r$, where $r$ is the radius and $\pi = \dfrac{{22}}{7}$.