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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.
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
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.
First, let's find the radius:
r=d2r=162r=8 \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.

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