Question

The diameter of the car wheel is \[{\text{70cm}}\]. How many revolution will it make to travel \[{\text{1}}{\text{.65Km}}\]

Answer 1

Hint: Distance that will be covered by the wheel in one turn will be equal to it’s circumference . And so it must be rolled several times in order to travel out total \[{\text{1}}{\text{.65Km}}\]. So equate them and calculate the number of turns.

Complete step-by-step answer:
First of all calculating the distance covered by the wheel in one rotation :
As per the given values ,
\[
  {\text{d = 70cm}} \\
  {\text{r = 35cm}} \\
 \]
And by substituting it in below formula we will get as calculated :
\[\therefore {{Circumference = 2\pi r}}\]
On substituting the value of r, we get ,
\[
  {{ = 2 \times (}}\dfrac{{{{22}}}}{{{7}}}{{) \times 35}} \\
  {{ = 2 \times 22 \times 5}} \\
  {{ = 220cm}} \\
  {{ = 2}}{\text{.2m}} \\
\]
Now , in total wheel has to keep rolling till it will cover \[{\text{1}}{{.65Km = 1}}{{.65 \times 1000m}}\]
So let the number of turns be n
\[
   \Rightarrow {{n(2\pi r)}} = 1.65 \times 1000 \\
   \Rightarrow {\text{n}}(2.2) = 1650 \\
   \Rightarrow {\text{n = }}\dfrac{{{\text{1650}}}}{{{\text{2}}{\text{.2}}}} \\
  \therefore {\text{n}} = 750 \\
 \]
Hence to cover \[{\text{1}}{\text{.65Km}}\] the wheel with \[{\text{70cm}}\] diameter has to rotate almost 750 times.

Note: A circle is a shape consisting of all points in a plane that are a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
The distance around a circle on the other hand is called the circumference (c). A line that is drawn straight through the midpoint of a circle and that has its endpoints on the circle border is called the diameter (d).