Question

If the driving wheel of a bicycle makes 560 revolutions in travelling 1.1 kilometers, what is its radius?

Answer 1

Hint: We will use the formula of circumference of the circle which is given as Circumference = \[2\pi r\], where r is the radius of the circle. We will apply the formula and substitute values to get the answer.

Complete step-by-step answer:
Given a driving wheel of a bicycle makes 560 revolutions in travelling 1.1 kilometers, we have to find the radius of the wheel.
Converting the given distance in kilometers we will convert it into centimeters.
Doing so we have,
1km= $10^5$cm
\[\Rightarrow \]1.1 km = 110000 cm.
Distance travelled in one revolution, will be \[=\dfrac{\text{distance travelled}}{\text{number of revolutions}}\]
Substituting the values in above equation we get,
Distance travelled in one revolution, will be \[=\dfrac{110000}{560}\]
\[\Rightarrow \dfrac{110000}{560}=\dfrac{1375}{7}\].
Therefore, distance travelled in one revolution is \[\dfrac{1375}{7}\]
We know that, Circumference of wheel = \[2\pi r\], where r is the radius of the circle.
Also, Circumference of wheel = Distance travelled in one revolution
\[\Rightarrow 2\pi r=\dfrac{1375}{7}\]
\[\Rightarrow 2\left( \dfrac{22}{7} \right)(r)=\dfrac{1375}{7}\] [value of \[\pi \] = \[\dfrac{22}{7}\]]
\[\Rightarrow \dfrac{44}{7}(r)=\dfrac{1375}{7}\]
\[\begin{align}
  & \Rightarrow r=\left( \dfrac{1375}{7} \right)\left( \dfrac{7}{44} \right) \\
 & \Rightarrow r=31.25cm \\
\end{align}\]
Therefore, the radius of the given wheel is 31.25 centimeters.

Note: Always to solve such questions convert the units of all the given variables or terms as one single same unit and then proceed to solve the question. Preferable convert in centimeters to solve the question.