Whats the area of a circle if the radius is 12?

2 Answers
Mar 13, 2018

The area of the circle is #452#.

Explanation:

The formula for the area of a circle is:

#A=pi*r^2#

#pi# should be a key on your calculator. If not, use #3.14#. Plug in the value for the radius and solve.

#A=pi(12)^2#

Simplify.

#A=pi*144#

#A=452#

Mar 13, 2018

#144pi ~~ 452.39#

Explanation:

The area of a circle with radius #r# is #pi r^2#

So if #r=12# then the area is: #pi * 12^2 = 144pi#

Bonus

Why is the area of a circle given by the formula #pi r^2# ?

All circles are similar. So the ratio between the circumference and the diameter is always the same. We call that ratio pi, represented by the Greek letter #pi#. The radius is half of the diameter, so the circumference of a circle of radius #r# is #2pi r#.

To find the area of a circle, we can split it into equal segments and rearrange them head to tail to form a sort of bumpy parallelogram.

The length of the base of the parallelogram will be about #1/2# of the circumference of the circle, i.e. #pi r#, while its height will be about #r#. So the area of the bumpy parallelogram is shown to be about #r * pi r = pi r^2#.

This works better the smaller the segments, but here's an animated illustration I constructed with just #8# segments...

enter image source here