Question

What is the approximate area of a circle with the radius of 1.5 ?

Answer 1

`9pi`

Explanation:

Area of a circle is `pi r^2`.

We're given the radius. Plug it into the formula:

`pi (1.5)^2=2.25pi`

That's the area of `1` circle we have four circles. So multiply this by `4`"

`2.25pi (4)=9pi`

Answer 2

Further comment

Explanation:

There are a set of 'special' numbers that crop up all over the place and are very useful. One of them is `pi`

`pi` is the number you get if you divide the circumference of a circle by its diameter. So in effect it is a ratio. It also occurs a lot in nature.

This is what is called an irrational number. This is just a name! An irrational number is one that that has decimal values that go on for ever without any repeats. I just did a quick search and found a listing of 100,000 digits. Part of which is:

3.1415926535897932384626433832795028841971693993
75105820974944592307816406286 ....

The dots at the end mean that the digits go on a lot further.

Go back enough in time and it used to be taught that an approximation of this value is `22/7` this works out to be 3.142857...

Comparing `22/7` to 3.141562... you will observe that it starts to be different at the 3rd decimal place.

As against `22/7` a more precise approximation of `pi` is 3.142 which is rounded to 3 decimal places
It all depends on how precise an approximation you require. It could be argued that just the value of 3 is also an approximation.

Hope this helps

By the way: when you round a decimal it is good practice to state the number of decimal places it is rounded to. That way it indicates the potential error that creeps into the calculation.