How do you find the area of a circle?

[jim1174]

If you have a circle with a line that divided it in half. The Internet sites say to take the number and cut it in half like if it was 10 you do 314 x 5 x 5. My textbook says to do 314x 10

 

[jfizzix]

If you have a circle, you can find its area by:

First: Cutting the circle in half right through the center.
The straight line going from one side of the circle to the opposite end is called its diameter.
Half of this diameter is the distance a straight line makes from the center of the circle to the edge. This half-distance is called the radius.

To find the area of a circle, we can take the number $\pi$, which is about 3.14, and multiply that by the radius $r$, and then by the radius again.

This gives you the formula for the area $A$, of a circle, which is:
$A = \pi \times r\times r = \pi r^{2}$

Your textbook might be saying $r^{2}$ instead of $r\times r$.
When the 2 is to the right of the $r$, and raised up like a little super script, that means you multiply by $r$ two times. It's a bit of mathematical shorthand called an exponent.

As an example, it's easier to write $n^{5}$ than $n\times n\times n\times n\times n$. Makes life easier in the long run.

 

[Mentallic]

If you have a circle with a line that divided it in half. The Internet sites say to take the number and cut it in half like if it was 10 you do 314 x 5 x 5. My textbook says to do 314x 10

You're writing 314 when it should be 3.14 (314 is 100 times more than 3.14). Also don't forget about the units.

Let's say that you have a big circle on the ground that's 1m in diameter, so it's 0.5m in radius, then the area of the circle is

$$A=\pi r^2=3.14\times 0.5\times 0.5 = 0.785m^2$$

Notice the units at the end: m² which means the area of the circle is a little over 3/4 of a meter squared.
If we instead decided to measure the radius in cm, being 50cm, then our answer is

$$A=3.14\times 50^2 = 7,850cm^2$$

Which is the same answer, but with different units.

 

[Mark44]

In addition to what others have said, 3.14 is a very poor approximation to $\pi$. Most scientific calculators these days have a button for $\pi$ that gives this number to 10 or more decimal places.

 

[HallsofIvy]

If you have a circle with a line that divided it in half. The Internet sites say to take the number and cut it in half like if it was 10 you do 314 x 5 x 5.

Except for the missing decimal point, that is correct. The area of a circle with radius "r" is $\pi r^2$ where "$\pi$" is a constant that is, to two decimal places, 3.14.

My textbook says to do 314x 10

The circumference of a circle of diameter "d" is $\pi d$ (or in terms of radius r, $2\pi r$). That's probably what your textbook is talking about.