Question

The diameter of the wheel of a car is 70cm. How many revolutions will it make to travel 1.65 km?

Answer 1

Hint: First find the radius of the wheel which is half the diameter. Use the radius of the wheel to find the circumference of the wheel which will be equal to the distance of one revolution. Determine the number of revolutions by dividing the total distance by circumference of the wheel.

Complete step-by-step answer:
We are given that the diameter of the wheel is 70 cm.
We know that radius is half the diameter.

Thus, the diameter of the wheel is $\dfrac{{70}}{2} = 35cm$
We will calculate the distance in one revolution by determining the circumference of the wheel.
Circumference of the wheel is given by $2\pi r$, where $r$ is the radius of the wheel.
Then the distance covered in one revolution
is:
$\Rightarrow$ $2\left( {\dfrac{{22}}{7}} \right)\left( {35} \right) = 220cm$
We will divide it by 10,000 to convert it into km
$\Rightarrow$ $\dfrac{{220}}{{10,0000}}km$
Hence, $\dfrac{{220}}{{10,0000}}km$ is covered in 1 revolution.
Then, we will divide the given distance by distance covered in one revolution to find the number of revolutions.
$\Rightarrow$ $\dfrac{{1.65}}{{220}} \times 100000 = 750$
Thus, the total number of revolutions is 750 .

Note: The circumference of the circle is the length of the boundary of the circle. When a wheel completes one revolution it covers the distance equals to its circumference of a circle.