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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:
$\text{Area of circle}=\pi ×{\text{radius}}^{2}$
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 $5$.
The equation for the area of a circle is:
$A=\pi {r}^{2}$
$A=\pi \cdot {5}^{2}$
$A=\pi \cdot 25$
We can stop here and write our answer as $25\pi$. Or we can plug in $3.14$ for $\pi$ and multiply.
$A=3.14\cdot 25$
$A=78.5$ square units
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 $16$.
$\begin{array}{rl}r& =\frac{d}{2}\\ \\ r& =\frac{16}{2}\\ \\ r& =8\end{array}$
Now we can find the area.
The equation for the area of a circle is:
$A=\pi {r}^{2}$
$A=\pi \cdot {8}^{2}$
$A=\pi \cdot 64$
We can stop here and write our answer as $64\pi$. Or we can plug in $3.14$ for $\pi$ and multiply.
$A=3.14\cdot 64$
$A=200.96$ square units
The area of the circle is $64\pi$ square units or $200.96$ square units.

## Practice

Problem 1
Find the area of a circle with a radius of $7$.
Either enter an exact answer in terms of $\pi$ or use $3.14$ for $\pi$ and enter your answer as a decimal.
units${}^{2}$

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!
• i like math

*sobs in the corner while trying to find the answer*
• no cap
• 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!
• 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)
• '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.'
• I like to use 3.14
• this no fun
• 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!
• 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