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Circumference of A Circle: Definition and Examples | EDU.COM

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Circumference of A Circle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Circumference of A CircleCircumference of A Circle: Definition and ExamplesTable of ContentsCircumference of a Circle Definition of Circumference of a Circle

The circumference is the length of the boundary of a circle. It is also known as the "perimeter" of a circle. Since it represents length, it is measured in units of lengths such as feet, inches, centimeters, meters, miles, or kilometers. All points on the boundary of a circle are at an equal distance from its center, and this distance is called the radius.

The ratio of the circumference to the diameter of any circle is a constant called pi (denoted by π\piπ). For all circles, regardless of small or big, this ratio remains constant. The approximate value of π\piπ is 3.143.143.14 or 227\frac{22}{7}722​. Using this constant, we can calculate the circumference of a circle with the formula C=πdC = \pi dC=πd when the diameter is given, or C=2πrC = 2\pi rC=2πr when the radius is given, where CCC is the circumference, ddd is the diameter, and rrr is the radius.

Examples of Finding the Circumference of a Circle Example 1: Finding Circumference from Diameter Problem:

What is the circumference of a circle with a diameter of 141414 feet? Use π=3.14\pi = 3.14π=3.14.

Step-by-step solution:

Step 1, Write down what we know. The diameter (ddd) = 141414 feet.

Step 2, Recall the formula for circumference when diameter is known. The formula is C=πdC = \pi dC=πd, where CCC is the circumference.

Step 3, Put the values into the formula and solve. C=πd=3.14×14C = \pi d = 3.14 \times 14C=πd=3.14×14 feet

Step 4, Calculate the final answer. C=43.96C = 43.96C=43.96 feet

Example 2: Finding Circumference from Radius Problem:

The radius of a circle is 666 inches. What is the circumference of the circle? Use π=3.14\pi = 3.14π=3.14.

Step-by-step solution:

Step 1, Write down what we know. The radius (rrr) = 666 inches.

Step 2, Recall the formula for circumference when radius is known. The formula is C=2πrC = 2\pi rC=2πr, where CCC is the circumference.

Step 3, Put the values into the formula and solve. C=2πr=2×3.14×6C = 2\pi r = 2 \times 3.14 \times 6C=2πr=2×3.14×6 inches

Step 4, Calculate the final answer. C=37.68C = 37.68C=37.68 inches

Example 3: Finding Radius from Circumference Problem:

The circumference of a circle is 120120120 m. Find its radius. Use π=3.14\pi = 3.14π=3.14.

Step-by-step solution:

Step 1, Write down what we know. The circumference (CCC) = 120120120 m.

Step 2, Recall the formula that connects circumference and radius: C=2πrC = 2\pi rC=2πr

Step 3, Put the known value into the formula. 120=2πr120 = 2\pi r120=2πr

Step 4, Solve for rrr by dividing both sides by 2π2\pi2π.

1202π=r\frac{120}{2\pi} = r2π120​=r

1202×3.14=r\frac{120}{2 \times 3.14} = r2×3.14120​=r

1206.28=r\frac{120}{6.28} = r6.28120​=r

Step 5, Calculate the final answer. r=19.11r = 19.11r=19.11 m

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