Please also find in the section below several worksheets and solutions on this topic to help your understanding. A circle is 360 degrees, so when you place the measurement of the sector's central angle over 360, it gives you the fraction of the whole circle. Click the links below to download your free worksheets and answer key: CLICK HERE TO DOWNLOAD YOUR FREE WORKSHEET. In this video, I explain the definition of a sector and how to find the sector area of a circle. Evaluating Expressions . where 'l' is the length of the minor arc AB. *This lesson guide accompanies our animated Arc Length and Sector Area Explained! To understand how to calculate the area of such a sector, it’s important to understand the formula that it uses, which is given above. ): The area of a circle is calculated as A = πr². Note: A circular sector or circle sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. Examples to find the angle of a sector given its area or arc length. Every day at wikiHow, we work hard to give you access to instructions and information that will help you live a better life, whether it's keeping you safer, healthier, or improving your well-being. Our sector area calculator can help you calculate the area of a sector. What is the sector area equation? Then, the area of a sector of circle formula is calculated using the unitary method. Note: Trying to find the area of a sector of a circle? Info. How to Calculate The Area of Sector with This Tool? Tutorial where you will learn the answers to the following key questions and information: What is the arc length formula? Double the radius, then multiply by pi. To calculate the sector area, first calculate what fraction of a full turn the angle is. How do I find the area if I only know the radius? Circle; Perimeter; Polygons; Quadrilaterals; Special Points; Discover Resources. Read more. Typically, the formula to calculate area of sector of a circle is A = pi *r 2. What is the sector area formula? Finally, multiply .28 by 78.5 for a final answer of 21.89, which is the area of the sector. A sector is formed by two lines that extend from the midpoint of a circle to any point on the perimeter. What is the central angle if the radius is 7 cm and the area of a sector is 15 cm squared? Share your thoughts in the comments section below! In this example, θ is the measure of angle ∠AKB, (the central angle of the green region), but the question only tells you that ∠AKC = 117 degrees. Your support helps wikiHow to create more in-depth illustrated articles and videos and to share our trusted brand of instructional content with millions of people all over the world. If you know the length of the arc (which is a portion of the circumference), you can find what fraction of the circle the sector represents by comparing the arc length to the total circumference. It’s a percent or portion of a disk that is enclosed by that arc and two equal radii. When angle of the sector is 360°, area of the sector i.e. Before you can use the Sector Area Formula, you will have to find the value of θ (the central angle that intercepts arc AB, which is the arc of the shaded region ) and the length of the radius of circle K. In the formula given, A is the area of the sector, N is the degree of the central angle of the sector, pi is an irrational number that can be rounded to 3.14, and r is the length of the radius of the circle. The area will be expressed in square feet. Then check out this tutorial! The Area of A Sector Calculator is used to help you find the area of a sector of a circle. There are two special cases. This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. About this resource . The only two ways of finding a sector's area are shown above. Sol. The arc length l and area A of a sector of angle θ in a circle of radius r are given by The angle between the two radii is called as the angle of surface and is used to find the radius of the sector. Question 8 : Find the area of the sector whose radius is 20 cm and perimeter is 110 cm. Please help us continue to provide you with our trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker. Formula to find perimeter of the sector is = l + 2r. Whenever you want to find the length of an arc of a circle (a portion of the circumference), you will use the arc length formula: Where θ equals the measure of the central angle that intercepts the arc and r equals the length of the radius. An arc is a part of the circumference of the circle. Find the length of its arc and area. Whenever you want to find area of a sector of a circle (a portion of the area), you will use the sector area formula: Now that you know the formulas and what they are used for, let’s work through some example problems! Therefore, the central angle is equal to the sector area multiplied by 360° and then divided by πr². Since you are finding the area, the answer will be in square centimeters. First, we figure out what fraction of the circle is contained in sector OPQ: , so the total area of the circle is . To find the area of the segment, you find the area of the sector. And, since you know that diameter JL equals 24cm, that the radius (half the length of the diameter) equals 12 cm. But, if we measure the angle of a circle in radians, the area of sector formula will be AreaofSectorAreaof… We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. To solve this, we must begin by finding the area of the diagram, which is the area of the square less the area of the semicircle. Welcome to this free lesson guide that accompanies this Arc Length and Sector Area Explained! radius r = 18 cm. Or spending way too much time at the gym or playing on my phone. or A = rl / 2 square units. Remember the formula for finding the circumference (perimeter) of a circle is 2r. This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Find the area of sector IDK. Now we have the length of an arc and radius. 350 divided by 360 is 35/36. A = 60° / 360° × 3.14 × 25 A = 60° / 360° × 78.5 A = 0.166 × 78.5 = 13.06 cm 2 Example #2: A pizza has a diameter of 14 inches. Step by step calculation. A sector is a part of a circle that is shaped like a piece of pizza or pie. A circular sector or circle sector (symbol: ⌔), is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. To find the area of a sector of a circle of radius of 4 centimeters and central angle measure of : Step 1: Find the area of the circle. To understand how to calculate the area of such a sector, it’s important to understand the formula that it uses, which is given above. Sector area formula. Find the length of its arc and area. For more on this seeVolume of a horizontal cylindrical segment. You can find it by using proportions, all you need to remember is circle area formula (and we bet you do! We can use this to solve for the circumference of the circle, , or . Measuring the diameter is easier in many practical situations, so another convenient way to write the formula is (angle / 360) x π x (diameter / 2)2. You can often find me happily developing animated math lessons to share on my YouTube channel . References. Before you learn the arc length equation and the area of a sector equation, let’s quickly review two very important (and very familiar) circle properties: Circumference and Area. Now that you know the value of θ and r, you can substitute those values into the Arc Length Formula and solve as follows: Notice that this question is asking you to find the area of a sector of circle K, so you will have to use the Sector Area Formula to solve it! In the case of arc length and sector area, you will only be dealing with a portion of a circle. As shown in Method 1 above, the sector area equals the central angle divided by 360° and then multiplied by πr². Doing … The area of a sector along an arc is also known as the circular sector. Trying to find the area of a sector of a circle? How to Calculate the Area of a Sector of a Circle. We use cookies to make wikiHow great. Step 2: Use the proportional relationship. All tip submissions are carefully reviewed before being published, This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Calculating the Area with a Known Central Angle and Radius, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/4\/4b\/Calculate-the-Area-of-a-Sector-Step-1.jpg\/v4-460px-Calculate-the-Area-of-a-Sector-Step-1.jpg","bigUrl":"\/images\/thumb\/4\/4b\/Calculate-the-Area-of-a-Sector-Step-1.jpg\/aid1517870-v4-728px-Calculate-the-Area-of-a-Sector-Step-1.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"

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