Question

The diameter of a bicycle wheel is 28 cm. What distance will it cover in 100 revolutions?

Answer 1

Hint:
First, we will take the shape of the circle for finding the revolutions as when the wheel of the bicycle will rotate means the circle is going to cover the distance. Then we will use the formula of the circumference of the circle is \[2\pi r\], where \[r\] is the radius and then we will multiply it to 100 to find the distance.

Complete step by step solution:
We are given that the diameter \[d\] of a roller is 28 cm.
First, we will take the shape of the circle for finding the revolutions as when the wheel of the bicycle will rotate means the circle is going to cover the distance.

We will now find the radius \[r\] of the given roller from the above value of diameter of a wheel.
\[
   \Rightarrow r = \dfrac{{28}}{2}{\text{ cm}} \\
   \Rightarrow r = 14{\text{ cm}} \\
 \]
We will use the formula of the circumference of a circle is \[2\pi r\], where \[r\] is the radius.
Substituting the values of \[r\] in the above formula of circumference of circle, we get
\[
   \Rightarrow {\text{Circumference of circle = }}2 \times \dfrac{{22}}{7} \times 14 \\
   \Rightarrow {\text{Circumference of circle = }}2 \times 22 \times 2 \\
   \Rightarrow {\text{Circumference of circle = }}88{\text{ cm}} \\
 \]
Since we know that the distance covered by a wheel in one revolution is the same as the circumference of the circle.
Thus, the distance covered in 1 revolution is \[88{\text{ cm}}\].
We will now find the distance covered by the wheel in 100 revolutions from the above value.
\[ \Rightarrow 88{\text{ cm}} \times 100 = 8,800{\text{ cm}}\]

Therefore, the distance covered by the wheel of the bicycle in 100 revolutions is 8,800 cm.

Note:
We need to know that only in case of a circle or the wheel distance covered is the circumference of the circle. We do not need to find the area of the wheel, as it will be useless. Do not rush finding the distance covered in 100 revolutions or else the answer may be wrong. Avoid calculation mistakes.