Question

A bicycle wheel makes 5000 revolutions in moving 11km. Find the diameter of the wheel.

Answer 1

Hint: As the question mentions that the wheel is moving, we have to find the circumference of the wheel. You have to find the diameter in meters or centimeters. First convert the measure unit in the meter or centimeter. Use the value of $\pi = \dfrac{{22}}{7}$.

Complete step-by-step answer:
First, we right the given information,
Now let the r is the radius of the wheel
Distance of the wheel travel =$11km$
Number of the revolution it makes = $5,000$
Circumference of the circle is $ = 2\pi r$
Distance covered in 1 resolution $ = 2\pi r$.
So, we have to find the distance covered in one revolution
$ = 2\pi r$
Put the value of $\pi $
$ = 2.\dfrac{{22}}{7}.r$
We have to find the 5000 revolution in moving 11km
First, we have to convert the km into m
1m = 1000km
11km = 11 .1000 m
=11000m
Now putting the values in the formula, we get
We multiplied by 5000 because we are calculating the distance covered in 5000 revolutions, and we equated the equation to 11000 because it is given that the distance travelled in 5000 revolutions is 11000m.
$5000.2.\dfrac{{22}}{7}.r = 11000$
$5000.\dfrac{{22}}{7}.2r = 11000$
$2r = \dfrac{{11000.7}}{{5000.22}}$
$2r = \dfrac{7}{{10}}$m
We known that 2r is equal to diameter or we can say r + r = diameter

So, now we have the diameter of the wheel as $\dfrac{7}{{10}}m$.

Note: In this question the student does not convert the measure unit which leads to the wrong answer. Put the value of $\pi = \dfrac{{22}}{7}$ instead of 31.4 to make the calculation simple. In this question we have to find the circumference of the wheel so students get confused between the area and the circumference formula of the circle first read the question as the question mentions the wheel is moving so we have to find the circumference.