Question

How do you find the area of a circle with a radius of 3.2 centimeters?

Answer 1

Area of circle = 32.183 cm^2

Explanation:

Area of circle formula is `pir^2` where `pi=22/7` and r is the radius of the circle.
Given `r=3.2` cm
Area of circle `=(22/7)*(3.2)^2=(22*3.2*3.2)/7=32.183 cm^2`

Answer 2

`"Area" ~~ 32.17 "cm"^2`

Explanation:

The area of a circle of radius `r` is given by the formula:

`"Area" = pir^2`

In our example, `r = 3.2 "cm"`, so:

`"Area" = pir^2 = pi(3.2"cm")^2 = 10.24 pi "cm"^2`

It probably suffices to use the approximation `pi ~~ 3.1416` to find:

`"Area" = 10.24 pi "cm"^2 ~~ 10.24*3.1416 "cm"^2 ~~ 32.17 "cm"^2`

Bonus

Why is the area of a circle given by the formula `"Area" = pir^2` ?

All circles are similar, so the ratio between the circumference and the diameter is always the same, namely the number `pi ~~ 3.1415926536`. The radius is half the diameter, so in terms of the radius `r`, the circumference is `2pir`.

Given a circle, we can dissect it into a number of segments of equal size and reassemble them head to tail into a sort of bumpy parallelogram. This parallelogram will have base of length approximately `pir` (being half of the circumference of the circle) and height `r`. So its area will be `pir * r = pir^2`.

It works better the more segments you use, but here's an animation I made that illustrates using just `8` segments...