Question

A bicycle wheel travels \[82inches\] in \[1\] full rotation. What is the diameter of the wheel?

Answer 1

Hint: Since in this question we have to find the diameter of wheel and we know that diameter is always calculated as two times of radius of the wheel .Here radius is not given directly we have to find the radius of the wheel by using the concept of how much distance is covered in one full rotation of the wheel.

Complete step-by-step solution:
Since in one complete rotation of the wheel or any circular object, it always covers a distance equal to the circumference of the circular wheel or that circular object.
Let us assume the radius of that circular wheel as\[R\].
Then the distance or straight path covered by that circular wheel in one complete full rotation\[=2\pi R\].
And diameter is always equal to two times the radius of any circular object.
Here in this question it is mentioned then in one full rotation the circular wheel travels\[82inches\].
So this distance or straight path covered is equivalent to the circumference of the circular wheel as we define in the above paragraph.
Now, Let us assume the radius of this given circular wheel is\[R\].
Circumference of this circular wheel\[=2\pi R\].
Then according to the question we can write mathematically –
\[2\pi R=82\]
On simplifying this equation we get the value of radius of wheel.
\[R=\dfrac{82}{2\pi }\]- - - - - - - - -Equation (1)
Since the value of \[\pi =\dfrac{22}{7}\]put this value in above equation 1 then we get,
 \[\begin{align}
  & R=\dfrac{82\times 7}{2\times 22} \\
 & \Rightarrow R=\dfrac{574}{44} \\
 & \therefore R=13.04inches \\
\end{align}\]
Now we have to calculate the diameter of this circular wheel and we know that the diameter of the wheel is expressed as two times of the radius of that circular wheel.
Let us assume the diameter of the wheel is represented as\[D\].
So mathematically we can write as:-
\[D=2R\]
Put the value of \[R\]from above we get,
\[\begin{align}
  & D=2\times 13.04 \\
 & \therefore D=26.08inches \\
\end{align}\]
So at last we can conclude that the diameter of the wheel is \[26.08inches\]or on rounding off we can also write it as\[26inches\].

Note: For a moving body distance is always greater than or equal to displacement, for any kind of motion distance is found more than displacement, when body after travelling come back to initial point of motion the displacement is found to be zero but distance can never be zero if body is moving because it represents the total actual path travelled.