Question

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

Answer 1

Hint: A circular shaped bicycle wheel makes 5000 revolutions, which means that the wheel has moved 5000 times around its circumference. This implies that we need to find how much distance the wheel has covered in 1 revolution, which will give us the circumference of the bicycle wheel. The formula of finding the circumference of a wheel is $2\pi\text{ r}$, where r is the radius of the bicycle wheel. Thus, we get the radius of the cycle by solving the equation, and consequently also get the diameter.

Complete step-by-step answer:
It is given that the bicycle wheel makes 5000 revolutions in moving 11 km.
This implies that in order to make 1 revolution, the distance covered by the wheel
$\begin{align}
  & =\text{ }\dfrac{11}{5000}\text{ km}\text{.} \\
 & \text{= }\dfrac{11000}{5000}\text{ m}\text{.} \\
 & \text{= }\dfrac{11}{5}\text{ m}\text{.} \\
\end{align}$
Thus, the wheel covers $\dfrac{11}{5}\text{ m}\text{. }$ to make one revolution. Since, to complete one revolution, a circular object needs to move around its circumference once, we can simply say that,
Circumference of the bicycle wheel $=\text{ }\dfrac{11}{5}\text{ m}\text{.}$
We know the formula for the circumference of a circular object is given by the formula $2\pi\text{ r}$, where r is the radius of the object.
Here, let us assume the radius of the bicycle wheel be ‘r’ m.
Then, according to the problem,
$\begin{align}
  & 2\pi\text{ r = }\dfrac{11}{5} \\
 & \Rightarrow \text{ }2\text{ x }\dfrac{22}{7}\text{ x r = }\dfrac{11}{5}\text{ }\left( \because \text{ we use }\pi \text{ = }\dfrac{22}{7} \right) \\
 & \therefore \text{ r = }\dfrac{11}{5}\text{ x }\dfrac{7}{22\text{ x 2}} \\
 & \text{ = }\dfrac{7}{20}\text{ } \\
\end{align}$
Hence, we get the radius of the bicycle wheel as $\dfrac{7}{20}\text{ m}\text{.}$
$\therefore $ Diameter of the bicycle wheel
$\begin{align}
  & =\text{ 2 x }\dfrac{7}{20}\text{ m}\text{.} \\
 & \text{= }\dfrac{7}{10}\text{ m}\text{.} \\
 & \text{= 0}\text{.7 m}\text{.} \\
\end{align}$
Thus, the diameter of the bicycle wheel is 0.7 m.

Note: If a circular object of radius r makes n revolutions, then it moves a total distance of n x $2\pi \text{ r}$.