Main content

## 7th grade

### Course: 7th grade > Unit 9

Lesson 1: Area and circumference of circles- Geometry FAQ
- 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
- Partial circle area and arc length
- Circumference of parts of circles
- Area of parts of circles
- Circumference review
- Area of circles review

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# 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 start color #11accd, 5, end color #11accd.**

The equation for the area of a circle is:

A, equals, pi, r, squared

A, equals, pi, dot, start color #11accd, 5, end color #11accd, squared

A, equals, pi, dot, 25

A, equals, pi, dot, start color #11accd, 5, end color #11accd, squared

A, equals, pi, dot, 25

We can stop here and write our answer as 25, pi. Or we can plug in 3, point, 14 for pi and multiply.

A, equals, 3, point, 14, dot, 25

A, equals, 78, point, 5 square units

A, equals, 78, point, 5 square units

The area of the circle is 25, pi square units or 78, point, 5 square units.

### Example 2: Finding area when given diameter

**Find the area of a circle with a diameter of start color #1fab54, 16, end color #1fab54.**

First, let's find the radius:

Now we can find the area.

The equation for the area of a circle is:

A, equals, pi, r, squared

A, equals, pi, dot, start color #11accd, 8, end color #11accd, squared

A, equals, pi, dot, 64

A, equals, pi, dot, start color #11accd, 8, end color #11accd, squared

A, equals, pi, dot, 64

We can stop here and write our answer as 64, pi. Or we can plug in 3, point, 14 for pi and multiply.

A, equals, 3, point, 14, dot, 64

A, equals, 200, point, 96 square units

A, equals, 200, point, 96 square units

The area of the circle is 64, pi square units or 200, point, 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.(31 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!(28 votes)

- i like math

***sobs in the corner while trying to find the answer***(17 votes) - How could I get the exact circumference? Is it possible(5 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.(21 votes)

- Area is much simpler than i expected. Once you've remembered the formula it becomes very easy!(10 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)(2 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.'(7 votes)
- I like to use 3.14(3 votes)

- im so done my teacher bad(6 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(3 votes)

- My teacher would not teach us this yet I have NO idea what this means or what to do(3 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(7 votes)

- 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.(1 vote)
- 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.(6 votes)

- Is the area of a circle is pi×r squared or 2 pi r. I am confused. Thanks to those who respond.(2 votes)
- Remember that circumference (which is a distance) has length units, and area has square length units. Because the radius r has length units, the previous sentence should help you remember that circumference is 2 pi r, and area is pi r^2.

Have a blessed, wonderful day!(9 votes)