Question

The diameter of a wheel is \[1.26\] cm. What is the distance covered in \[500\] revolution.

Answer 1

Hint: In this question we have to find the distance covered by the wheel in \[500\] rotation. We will use the fact that the distance covered by the wheel in one revolution is equal to the circumference of the wheel. First of all we find the radius of the wheel. Then we proceed by finding the circumference of the wheel and then multiplying the circumference by \[500\] to find the distance covered in \[500\] revolution.

Complete answer:
This question is based on the application of the circumference of a circle. Circle is a locus of points whose distance from a fixed point called centre is always constant. While circumference is the length of the outer boundary of the circle.
Consider the given question,
Given, The diameter of wheel \[ = \]\[1.26\]
We know that radius is half the diameter
i.e. radius \[ = \]\[\dfrac{{{\text{Diameter}}}}{2}\]
Hence radius of wheel \[ = \] \[\dfrac{{1.26}}{2} = 0.63\]cm
Since , Distance covered in one revolution is equal to the Circumference of the wheel
Hence, circumference of wheel is given by
Circumference \[ = 2\pi r\], where \[r\]is the radius of the wheel/circle.
Hence distance covered in one revolution \[ = \]\[2\pi r = 2 \times \dfrac{{22}}{7} \times 0.63\]cm
On solving, we have
Distance covered in one revolution \[ = \] \[39.6\]cm
Now distance covered in \[500\] revolution \[ = \] \[500 \times 39.6\]
On multiplying, we get
The distance covered in \[500\] revolution \[ = \] \[19800\]cm
On conversion in meter ( i.e. dividing by 100) we get, \[198\]m
Hence the distance covered in \[500\] revolution is \[198\]m.

Note:
To convert from centimetre to metre, we divide by \[100\]. For example, convert \[500\] cm into m. Therefore we divide by \[100\] to convert into m.
 i.e. \[500{\text{ cm }} = \dfrac{{500}}{{100}}{\text{ m}} = {\text{5 m}}\].
The value of \[\pi = \dfrac{{22}}{7}\]or \[3.14\].
Circumference of circle \[ = 2\pi r\] where \[r\] is the radius of the circle.