Question

If the driving wheel of a bicycle makes 560 revolutions in travelling 1.1 kilometres, what is its radius?
(a) 31.25 cm
(b) 27.25 cm
(c) 13.25 cm
(d) 25.25 cm

Answer 1

Hint: We will use the formula of circumference of the circle which is given by Circumference= \[2 \pi r \] , where r is the radius of the circle. Also we know the definition of revolution that it is the ratio of speed in meters and circumference of wheel in meters. We know that circumference of a wheel is equal to distance travelled in one revolution.

Complete step-by-step answer:
Converting the given kilometres into meters, that is \[1.1 \;km = 1.1 \times 1000 \;m \]
Because, \[1\;km = 1000 \;m \] .
By the definition we have that revolution it is the ratio of speed in meters and circumference of wheel in meters.
Expressing in mathematical form we get, \[ \Rightarrow { \text{revolution = }} \dfrac{{{ \text{speed in meters}}}}{{{ \text{circumference in meters}}}} \] .
The circumference of wheel is = \[2 \pi r \]
Speed or distance travelled = \[1.1 \times 1000\;m = 1100\;m \]
Wheel of a bicycle make the revolution=560
Substituting in above,
 \[ \Rightarrow 560 = \dfrac{{1100}}{{2 \pi r}} \]
Rearranging the equation,
 \[
    \Rightarrow r = \dfrac{{1100}}{{2 \pi \times 560}} \ \
     \ \
 \]
We know the value of \[ \pi \] and substituting we get,
 \[ \Rightarrow r = \dfrac{{1100}}{{2 \left( { \dfrac{{22}}{7}} \right) \times 560}} \]
 \[ \Rightarrow r = \dfrac{{1100 \times 7}}{{2 \times 22 \times 560}} \]
 \[ \Rightarrow r = 0.3125 \;m \]
But, the given options are in centimetre. So we convert it into metres by multiplying by 100.
Then we get, \[ \Rightarrow r = 31.25 \;cm \] .
The radius of the wheel is 31.25 cm.
So, the correct answer is “31.25 cm”.

Note: In this type of problem most of the time we get wrong answers because of conversion of metres into centimetres and centimetres into metres. Always make sure that units will be in S.I. units. That is why we converted kilometers into meters. If the given options are in meters then there is no need to convert it into centimetres.