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### Course: Basic geometry and measurement > Unit 10

Lesson 1: Area and circumference of circles- Radius, diameter, circumference & π
- Labeling parts of a circle
- Radius, diameter, & circumference
- Radius and diameter
- Radius & diameter from circumference
- Relating circumference and area
- Circumference of a circle
- Area of a circle
- Area of a circle
- Circumference review
- Area of circles review

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# Area of circles review

Review the basics of area of circles and try some practice problems.

## Area of a circle

The area of a circle is the amount of space the circle covers. We can also think of it as the total amount of space inside the circle.

To find the area of a circle, we can use the following formula:

*Want a review of circle vocabulary terms (like pi, radius, and diameter)? Check out this article or this video.*

*Want to learn more about finding area of circles? Check out this video.*

### Example 1: Finding area when given radius

**Find the area of a circle with a radius of**${5}$ .

The equation for the area of a circle is:

We can stop here and write our answer as $25\pi $ . Or we can plug in $3.14$ for $\pi $ and multiply.

The area of the circle is $25\pi $ square units or $78.5$ square units.

### Example 2: Finding area when given diameter

**Find the area of a circle with a diameter of**${16}$ .

First, let's find the radius:

Now we can find the area.

The equation for the area of a circle is:

We can stop here and write our answer as $64\pi $ . Or we can plug in $3.14$ for $\pi $ and multiply.

The area of the circle is $64\pi $ square units or $200.96$ square units.

## Want to join the conversation?

- I need help..... if the circumference is a low number like 2, doesn't that make the diameter and radius a decimal which also makes the area a decimal? If not, how do you do it? I just don't understand it.(41 votes)
- Well, actually it's quite simple!

When diameter is 2 cm

Then, Radius = 1cm

Therefore, A=(pi)r^2

=(pi)*r*r

=3.14*1*1

=3.14 (approx.)

But, if Radius < 1cm,

Then the value of r*r is also a decimal.

If, Diameter is 0.5cm

The r=2.5cm

Therefore, the Area is (pi)r^2

A = (pi)0.25*0.25

= 0.0625(pi)

There is no rule that if Radius or Diameter is a decimal, then the Area and the Circumference is also decimal but it ALMOST always shows up that way.

Even if it is a decimal no difference.

You just have to be careful with all those decimal points!(43 votes)

- i like math

***sobs in the corner while trying to find the answer***(41 votes) - How could I get the exact circumference? Is it possible(9 votes)
- That is a very interesting question. I don't think you can because the circumference of a number is pi times the diameter. Pi is never ending and computers can "only" find like 50 billion digits. I don't think any number multiplies into an infinitely long number perfectly.(29 votes)

- Area is much simpler than i expected. Once you've remembered the formula it becomes very easy!(13 votes)
- agreed. once you remember (pi)*radius^2 it's soo easy

especially if you don't try to use 3.14 and just put, for instance, 3(pi)(6 votes)

- 'Would you rather uses Pi as a term or to use 3.14? I would rather use it as a term because it's much more simple.'(10 votes)
- I like to use 3.14(6 votes)

- im so done my teacher bad(9 votes)
- the diameter is the radius but time 2, the radius is half of the diameter, and the circumference is the radius squared times by pi(5 votes)

- My teacher would not teach us this yet I have NO idea what this means or what to do(6 votes)
- If you dont get it the formula for area is r*r*3.14= a and the circumference is d*3.14= c

r= radius d= diameter c= circumference a= area(9 votes)

- Hey! So I need help with finding the area of parts of a circle. I noticed that most of these comments were five years ago...but if someone is here who can help me, then please do! Tysm!(10 votes)
- so bascially you find the diameter of the circle lest say it was 6 after that u multiply the diameter(6) by Pi or 3.14, so 6 x 3.14. but for area of a circle u have to find the radius basically the radius is half the diameter so I this case the radius is 3, after that u multiply the radius by itself so 3 x 3 after that u multiply that by Pi so 9 x 3.14, and there is u answer! hopes that helps! :)(1 vote)

- Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.(3 votes)
- That is a wrong Pi approximation, brob1.

Actual Pi = 3.14159265... The numbers after the decimal never repeat in a pattern because Pi is an irrational number.(8 votes)

- Math may not be fun, but it is very fundamental in our basic daily living!

Its awesome if its your favorite subject, but believe me, it's not really a very popular favorite subject!

Just do your best, and you will do well!(11 votes)