Question

The diameter of a tricycle wheel is 28 inches. Through what distance does its centre move during one revolution of the wheel?

Answer 1

Hint: We know that \[diameter=2\times radius\]. So, in this case we have \[diameter=28\text{ }inches\] so $radius=14\text{ inches}$. Now, we will find the perimeter of the circles, using formula $circumference=2\pi \times radius$ which will give us the distance travelled by the centre of the circle.

Complete step-by-step answer:
It is given in the question that the diameter of a tricycle wheel is 28 inches, then we have to find the distance the centre of the wheel covers during one complete revolution of the wheel.
Let us assume that the radius of the wheel be ‘r’ and the diameter of the wheel be ‘D’ then we know that \[diameter=2\times radius\], therefore, we have
$d=28inches$
$2\times r=28\text{ }inches$
Therefore, we get radius of the wheel as
$r=\dfrac{28}{2}=14\text{ }inches$
So, the radius of the wheel is 14 inches. Now we know that for a circle, $circumference=2\pi \times radius$ and the distance travelled by the centre is equal to the circumference of the circle.
Now, using the formula $circumference=2\pi \times radius$, we put radius $r=14\text{ }inches$ and $\pi =\dfrac{22}{7}$, we get
$circumference=2\times \dfrac{22}{7}\times 14$
On performing calculations we get circumference as
$circumference=2\times 22\times 2=88\text{ }inches$
Now we use a unitary method to convert 88 inches into centimetre. Basically a unitary method is a mathematical approach in which we will find the value of 1 unit and then multiply the value of 1 unit with the number of units.
We know that $1inch=2.54cm=0.0254metres$. Therefore using this conversion formula to convert the circumference or the distance covered by wheel into metres, we get
$1inch=0.0254m$
Therefore, we get
$88\text{ }inches=88\times 0.0254\text{ }metres=2.2352\text{ }metres$
Therefore, circumference of the wheel is 2.2353m and this is also the distance covered by the centre of the wheel. Or in other words, distance covered by the centre of the wheel = 2.2352 metres.

Note: Many times students may not get this question and they think that how can we find the distance travelled by centre of the wheel with its diameter only, and they may skip this type of question in exam. But, if we know the concept that distance covered in one revolution will be equal to the circumference of the wheel, then this question can be solved in just a few steps.