Perimeter and Area

Circumference and Area of a Circle

Terms Associated with Circles

The circumference of a circle is its "perimeter," or the distance around its edge. If we broke the circle and bent it into one flat line, the length of this line would be its circumference:

Circumference of a Circle

The diameter of a circle is a line segment from one point on the edge of the circle to another point on the edge, passing through the center of the circle. It is the longest line segment that cuts across the circle from one point to another. There are many different diameters, but they all have the same length:

Diameters of a Circle

The radius of a circle is a line segment from the center of the circle to a point on the edge of the circle. It is half of a diameter, and thus its length is half the length of the diameter. Again, there are many radii, but they all have the same length. In the following diagram, a, b, and c are all radii:

Radii of a Circle

The area of a circle is the total number of square units that fill the circle. The area of the following circle is about 13 units. Note that we count fractional units inside the circle as well as whole units.

Area of a Circle

Formula for the Circumference of a Circle

Mathematicians have discovered a special number, called pi (represented by Π), which is the ratio of the circumference of any circle to the length of its diameter. Π is roughly equal to 3.14--most scientific calculators have a "Π" button that will produce more digits. Π is a non- terminating, non- repeating decimal; thus, Π is an irrational number.

Since Π is the ratio of the circumference to the diameter, Π = c/d; c = Π×d; and d = c/Π; where c and d are the circumference and the diameter, respectively. The most important equations to remember are the last two.

Thus, to find the circumference of a circle, multiply the diameter by Π. If you know only the radius (a more likely scenario), multiply the radius by 2 to find the diameter: c = 2×Π×r. To find the diameter of a circle, divide the circumference by Π. Use 3.14 for Π.

Try it! Find a pan, trash can, or other large circular object. Measure around the edge, and then measure the diameter. The circumference divided by the diameter should be roughly equal to Π.

Formula for the Area of a Circle

Interestingly enough, Π is also the ratio between the area of a circle and the square of its radius. Thus, Π = A/r²; A = Π×r²; and r =

. The most important equation to remember is the middle equation, A = Π×r². Thus, to find the area of a circle, square the radius and multiply by Π. If the radius is unknown but the diameter is known, divide the diameter by 2 to find the radius.

Examples:

What is the circumference of a circle with diameter 5?
c = d×Π = 5×3.14 = 15.7

What is the circumference of a circle with radius 3?
d = 3×2 = 6;c = d×Π = 6×3.14 = 18.8

What is the area of a circle with radius 3?
A = Π×r² = 3.14×3² = 28.3

What is the area of a circle with diameter 5?
r = 5/2 = 2.5;A = Π×r² = 3.14×2.5² = 19.6

What is the diameter of a circle with circumference 11?
d = c/Π = 11/3.14 = 3.50

What is the radius of a circle with circumference 11?
r = d /2 = 3.50/2 = 1.75

What is the area of a circle with circumference 11?
A = Π×r² = 3.14×1.75² = 9.62