Question

A bicycle wheel makes 5000 revolutions in 11 km, find the diameter of the wheel.

Answer 1

Hint:Here, we know that the distance covered by a wheel in its one revolution is equal to its circumference. And given that distance covered in 5000 revolutions is equal to 11 km. Therefore, the distance covered is $5000\,revolutions = 5000\times$ circumference of the wheel, equate this value to 11 km and find its circumference. And using the formula of circumference of the circle or wheel we can find the diameter of the wheel.Change unit km to meter.

Complete step by step answer:
Given that the wheel makes 5000 revolutions to cover 11 km. We know that, distance covered by wheel in one revolution = Circumference of wheel
5000 revolutions = 11000 m [Since 1 km = 1000 m]
1 revolution = $\dfrac{{11000}}{{5000}}$ m
Circumference = $\dfrac{{11}}{5}$m [Since, distance covered in one revolution = circumference of circle]
$\pi d = \dfrac{{11}}{5}$ [Circumference of circle =$ \pi d$, where d is the diameter of the circle]
Putting the value of π.
$\dfrac{{22}}{7} \times d = \dfrac{{11}}{5}$
$ \Rightarrow d = \dfrac{{11}}{5} \times \dfrac{7}{{22}} \\
\Rightarrow d = \dfrac{7}{{10}} \\
\Rightarrow d = 0.7\,m\\
\Rightarrow d = 0.7 × 100 cm [ 1 m = 100 cm]\\
\therefore d = 70 cm$

Hence, the diameter of the wheel is $70\,cm$.

Note: In these types of questions, always equate the distance covered in revolutions to the given distance. Here, the wheel is like a circle and in one revolution, the circle covers a distance which is equal to its circumference. So, if a circle makes n revolutions, it will cover n times its circumference. Also, if we know the circumference of the circle we can easily find the diameter and radius of the circle. So, always try to find out the circumference of the wheel or circle.