Q1.
Here we see a circle with radius r units (Fig. 6.3). What is its perimeter? How do we find out?
Answer
The perimeter of a circle — its circumference — is 2πr units. Finding it is not like finding the perimeter of a square, because you cannot add up straight pieces.
Why it happens: for a square with side a, the perimeter is 4a: the ratio of perimeter to side is fixed at 4 : 1 for every square, large or small. For an equilateral triangle the ratio is 3 : 1 for every such triangle. The reason is the same in both cases — all squares are scaled copies of one another, and scaling multiplies every length by the same factor, so a ratio of two lengths cannot change.
All circles are also scaled copies of one another. So the ratio
circumference ÷ diameter = C/D
must be the same number for every circle. That number is what we call π. Once we know it, C = πD = 2πr. The work of the chapter is to find out what π is.
Try This: wrap a thread once round a cylindrical tin, then straighten the thread and measure it. Divide by the diameter of the tin. You should get something a little more than 3.