Question

How to solve the following ? When a car moves forward by $180\text{ cm}$ each wheel does one full turn. What is the diameter of a wheel to the nearest centimeter ?

Answer 1

Hint: When a car moves forward, all the wheels move uniformly. One wheel cannot make half a turn while the other three wheels make one full turn. So here in this question, when the car moves forward by a distance of $180\text{ cm}$, then and then only does one wheel make a full turn. So this means that the circumference of each wheel is equal to $180\text{ cm}$. So now we have to equate the formula of circumference of a circle to $180\text{ cm}$ and solve for the radius and then find out the diameter.

Complete step by step answer:
 As mentioned when the car moved forward by a distance of $180\text{ cm}$, the wheel took one complete turn. We inferred that the circumference of the wheel is equal to $180\text{ cm}$.
So now let us equate the formula of the circumference of the circle to $180\text{ cm}$.
Upon doing so, we get the following :
$\Rightarrow 2\pi r=180$
Where $r$ is the radius of the wheel.
Now let us substitute the value of $\pi $ and solve for $r$.
Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 2\pi r=180 \\
 & \Rightarrow 2\times \dfrac{22}{7}\times r=180 \\
 & \Rightarrow r=\dfrac{180\times 7}{22\times 2}=28.63 \\
\end{align}$
Now we got our radius of the wheel. Let us find out the value of the diameter of the wheel. We know the relation between radius and diameter.
$\Rightarrow d=2r$
Let us use that and find the diameter of the wheel.
$\Rightarrow d=2r=2\times 28.63=57.26$

$\therefore $ Hence, the diameter of a wheel to the nearest centimeter is $57.26\text{ cm}$.

Note: It is very important to be careful while solving as there is a lot of scope of calculation errors. We can take the value of $\pi $ to be either $3.14$ or $\dfrac{22}{7}$ according to the simplicity of our calculations. Notice that we have not changed the units from $cm$ to $m$ as we are asked to find out the diameter to the nearest centimeter. We should be careful with our units well while solving a question. We should remember all geometry formulae to complete the question quickly.