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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:
start text, A, r, e, a, space, o, f, space, c, i, r, c, l, e, end text, equals, pi, times, start text, r, a, d, i, u, s, end text, squared
Want a review of circle vocabulary terms (like pi, radius, and diameter)? Check out this article or 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
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
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.
\begin{aligned} r &= \dfrac d2 \\ \\ r &= \dfrac{\greenD{16}}{2} \\ \\ r &= \blueD{8} \end{aligned}
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
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
The area of the circle is 64, pi square units or 200, point, 96 square units.

## Practice

Problem 1
Find the area of a circle with a radius of start color #11accd, 7, end color #11accd.
Either enter an exact answer in terms of pi or use 3, point, 14 for pi and enter your answer as a decimal.
unitssquared

Want to try some more area of circle problems? Check out this exercise.

## 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.
• Well, actually it's quite simple!

When diameter is 2 cm
Therefore, A=(pi)r^2
=(pi)*r*r
=3.14*1*1
=3.14 (approx.)

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!
• How could I get the exact circumference? Is it possible
• 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.
• Area is much simpler than i expected. Once you've remembered the formula it becomes very easy!
• how do you find the area of a circle when given the circumference?
• circumference = 2 x pi x radius.
From there we get, radius = circumference / (2 x pi).
Now that we have the radius, we can plug it into the expression to find area.
(Area = pi x r x r).
• My teacher would not teach us this yet I have NO idea what this means or what to do
• 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
• im so done my teacher bad
• 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
• 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.
• 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.