Recall that the distance covered by travelling once around a circle is its perimeter, usually called its circumference. You also know from your earlier classes, that circumference of a circle bears a constant ratio with its diameter.
This constant ratio is denoted by the Greek letter `π` (read as `‘pi’` ). In other words,
`( text ( circumference) )/( text (diameter ) ) = pi`
or, circumference` = π × text ( diameter ) `
`= π × 2r` (where r is the radius of the circle)
`= 2πr`
The great Indian mathematician Aryabhatta (C.E. `476 – 550`) gave an approximate
value of `π`. He stated that `π = (62832)/(20000)` , which is nearly equal to 3.1416. It is alsom interesting to note that using an identity of the great mathematical genius Srinivas Ramanujan of India, mathematicians have been able to calculate the value of `π` correct to million places of decimals.
As you know, `π` is an irrational number and its decimal expansion is non-terminating and non-recurring (non-repeating).
However, for practical purposes, we generally take the value of `π` as `22/7` or `3.14`, approximately.
You may also recall that area of a circle is `πr^2`, where `r` is the radius of the circle. Recall that you have verified it in Class VII, by cutting a circle into a number of sectors and rearranging them as shown in Fig. 12.2
You can see that the shape in Fig. 12.2 (ii) is nearly a rectangle of length . `1/2 xx 2 pi r` and breadth `r`. This suggests that the area of the circle `= 1/2 xx 2 pi r xx r = pi r^2.`
Recall that the distance covered by travelling once around a circle is its perimeter, usually called its circumference. You also know from your earlier classes, that circumference of a circle bears a constant ratio with its diameter.
This constant ratio is denoted by the Greek letter `π` (read as `‘pi’` ). In other words,
`( text ( circumference) )/( text (diameter ) ) = pi`
or, circumference` = π × text ( diameter ) `
`= π × 2r` (where r is the radius of the circle)
`= 2πr`
The great Indian mathematician Aryabhatta (C.E. `476 – 550`) gave an approximate
value of `π`. He stated that `π = (62832)/(20000)` , which is nearly equal to 3.1416. It is alsom interesting to note that using an identity of the great mathematical genius Srinivas Ramanujan of India, mathematicians have been able to calculate the value of `π` correct to million places of decimals.
As you know, `π` is an irrational number and its decimal expansion is non-terminating and non-recurring (non-repeating).
However, for practical purposes, we generally take the value of `π` as `22/7` or `3.14`, approximately.
You may also recall that area of a circle is `πr^2`, where `r` is the radius of the circle. Recall that you have verified it in Class VII, by cutting a circle into a number of sectors and rearranging them as shown in Fig. 12.2
You can see that the shape in Fig. 12.2 (ii) is nearly a rectangle of length . `1/2 xx 2 pi r` and breadth `r`. This suggests that the area of the circle `= 1/2 xx 2 pi r xx r = pi r^2.`
