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Sector of A Circle: Definition and Examples | EDU.COM - AI智能索引
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Sector of A Circle: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Sector of A CircleSector of A Circle: Definition and ExamplesTable of ContentsSector of a Circle Definition of Sector of a Circle

A sector of a circle is a portion of a circle enclosed by two radii and an arc of the circle. It resembles the shape of a pizza slice, formed when two radii meet at the center and extend to the arc, which is a portion of the circumference. There are two types of sectors: minor and major. A minor sector contains the smaller area with an angle less than 180 degrees, while a major sector contains the greater area with an angle greater than 180 degrees.

The sector of a circle has specific formulas for calculating its area, perimeter, and arc length. When the angle is given in degrees, the area of a sector can be found using θ360∘×πr2\frac{\theta}{360^\circ} \times \pi r^2360∘θ​×πr2. If the angle is measured in radians, the area is 12×θ×r2\frac{1}{2} \times \theta \times r^221​×θ×r2. The perimeter of a sector equals 2r+θ360×2πr2r + \frac{\theta}{360} \times 2\pi r2r+360θ​×2πr. When the angle is not given but the arc length is known, the area can be calculated using lr2\frac{lr}{2}2lr​.

Examples of Sector of a Circle Example 1: Finding the Area of a Sector with a Given Angle Problem:

Calculate the area of the sector with radius 666 inches and angle 60∘60^\circ60∘.

Step-by-step solution:

Step 1, Identify what we know. The radius of the sector r=6r = 6r=6 inches and the angle of the sector θ=60∘\theta = 60^\circθ=60∘.

Step 2, Recall the formula for the area of a sector when the angle is given in degrees: Area of sector =θ360∘×πr2= \frac{\theta}{360^\circ}\times\pi r^2=360∘θ​×πr2

Step 3, Substitute the values into the formula to find the area:

Area of sector =60∘360∘×3.14×62=18.84= \frac{60^\circ}{360^\circ}\times3.14\times6^2 = 18.84=360∘60∘​×3.14×62=18.84 sq. in. Example 2: Finding the Area of a Sector in Radians Problem:

Find the area of a sector of a circular region whose central angle is 333 radians with a radius of 555 feet.

Step-by-step solution:

Step 1, Identify what we know. The radius of sector r=5r = 5r=5 feet and the angle of sector θ=3\theta = 3θ=3 radians.

Step 2, Recall the formula for the area of a sector when the angle is given in radians: Area of sector =θ2×r2= \frac{\theta}{2}\times r^2=2θ​×r2

Step 3, Substitute the values into the formula to find the area: Area of the sector =32×52=37.5= \frac{3}{2}\times5^2 =37.5=23​×52=37.5 sq. feet.

Example 3: Finding the Perimeter of a Sector Problem:

Find the perimeter of the sector with radius 888 inches and angle 115∘115^\circ115∘.

Step-by-step solution:

Step 1, Identify what we know. The radius of sector r=8r = 8r=8 inches and the angle of sector θ=115∘\theta = 115^\circθ=115∘.

Step 2, Recall the formula for the perimeter of a sector: Perimeter of sector =2r+θ360×2πr= 2r + \frac{\theta}{360}\times2\pi r=2r+360θ​×2πr

Step 3, Substitute the values into the formula:

=(2×8)+115∘360∘×(2×3.14×8)=(2\times8) + \frac{115^\circ}{360^\circ}\times(2\times3.14\times8)=(2×8)+360∘115∘​×(2×3.14×8)

Step 4, Simplify the calculation:

=16+(115360×50.24)=16 + (\frac{115}{360}\times50.24)=16+(360115​×50.24) =16+(0.319×50.24)=16 + (0.319 \times 50.24)=16+(0.319×50.24) =16+12.56=16 + 12.56=16+12.56 =28.56=28.56=28.56 inches Comments(4)MMathTutorAbbyNovember 6, 2025I've used this sector of a circle def for my students. It's clear & the examples help them grasp area & perimeter calcs easily. Thanks!

BBeautyGuruMiaNovember 5, 2025This glossary def on the sector of a circle is great! It helped my students grasp the concept easily. Thanks for the clear explanations!

BBoxerIsaacNovember 4, 2025This glossary page on the sector of a circle is great! I've used it to help my students grasp the concept. Clear defs and examples are super helpful.

NNatureLover75September 17, 2025I’ve been helping my kid with geometry, and this page explained sectors so clearly! The examples really made it click for them. Definitely bookmarking this for future math lessons.

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