Question

The diameter of a wheel is 28 cm. How many revolutions will it make to travel 352 m?

Answer 1

Hint: We are given the diameter of the wheel so; we will calculate the radius of the wheel. As we know that the distance in covering one revolution is equal to the circumference of the wheel which is the circle in shape that is \[2\pi r\]. Now, we will put the value of radius in the formula which will give us one revolution the wheel has to travel. Now, to find the number of revolutions to travel 352m is by dividing total distance by distance travelled in one revolution and thus get the desired result.

Complete step by step answer:

We will first consider the given data that is the diameter of the wheel is 28 cm and construct the figure,

Now, we will determine the value of radius by doing half of the given diameter,
Thus, we get,
\[
   \Rightarrow r = \dfrac{{28}}{2} \\
   \Rightarrow r = 14cm \\
 \]
Hence, the radius of the wheel is 14 cm.
Now, we will find the distance travelled to make one revolution.
As we know that the distance travelled in one revolution is equal to the circumference of the wheel which is given by \[2\pi r\].
Thus, now we will substitute the value of radius in above circumference,
Thus, we get,
\[ \Rightarrow 2\pi \left( {14} \right) = 88cm\]
Hence, to make one revolution the wheel has to travel 88 cm.
Now, we need to determine the number of revolutions to travel 352m.
So, as we have the total distance travelled and distance travelled to make one revolution, we will divide both the values one by one to determine the number of revolutions.
Also, the total distance is 352m so, we will convert it in cm by multiplying the value with 100.
\[ \Rightarrow 352 \times 100 = 35200cm\]
Thus, we get,
\[ \Rightarrow \dfrac{{35200}}{{88}} = 400\]
Hence, the number of revolutions taken to cover the given distance is 400.

Note: We can easily determine the radius from the given diameter of the wheel. For finding the number of revolutions, we have to divide total distance by distance travel in one revolution. remember the circumference of the circle that is \[2\pi r\]. Conversion of the unit from m to cm is necessary otherwise it will make the calculations wrong. Make the figure for a more clear solution. Do the substitutions properly in the formula.