# how to find area of a sector

A spherical sector is a solid portion of the sphere cut off by the plane. How do I find the area if I only know the radius? If the angle is 180 degrees then the sector is a semi-circle. Two further examples to find the radius of a sector given its area or arc length. The area of a sector along an arc is also known as the circular sector. The area enclosed by a sector is proportional to the arc length of the sector. 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. Area of the sector = (1/2) x l r square units = (1/2) x 77 x 35 ==> 38.5 x 35 ==> 1347.5 square units. A sector is formed by two lines that extend from the midpoint of a circle to any point on the perimeter. It’s a percent or portion of a disk that is enclosed by that arc and two equal radii. Please consider making a contribution to wikiHow today. You'll see how to use given information and the formula for the area of a sector to find the answer. A sector is a section of a circle. A sector is a part of a circle that is shaped like a piece of pizza or pie. Circle; Perimeter; Polygons; Quadrilaterals; Special Points; Discover Resources. sector angle θ = 25. where 'l' is the length of the minor arc AB. In the case of arc length and sector area, you will only be dealing with a portion of a circle. wikiHow's. Since you are finding the area, your answer will be in square centimeters. For example, if the radius is 5 cm, you will square 5 to get 25, and then multiply 25 by 3.14, to get 78.5. How to use Area of a Sector Calculator? 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. 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. What is the sector area formula? Then check out this tutorial! Therefore, to get the area of this slice of pizza, you will need to find the area of the circle and then divide the result by 4. Amid the current public health and economic crises, when the world is shifting dramatically and we are all learning and adapting to changes in daily life, people need wikiHow more than ever. The angle between the two radii is called as the angle of surface and is used to find the radius of the sector. Be careful, though; you may be able to find the radius if you have either the diameter or the circumference. or A = rl / 2 square units. Area of sector In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector. Sector area formula. by Anthony Persico. 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. Change the values of the angle of the sector and radius of the sector. The arc length l and area A of a sector of angle θ in a circle of radius r are given by Using this formula, and approximating , the area of the circle is . Related Topics. How do I find the area of a segment that does not have degrees? The formula for area, A A, of a circle with radius, r, and arc length, L L, is: A = (r × L) 2 A = (r × L) 2 Here is a three-tier birthday cake 6 6 inches tall with a diameter of 10 10 inches. A sector is an area formed between the two segments also called as radii, which meets at the center of the circle. Sector. *This lesson guide accompanies our animated Arc Length and Sector Area Explained! April 7, 2020 Write a Python program to calculate the area of a sector. The circumference of a circle is the linear distance around the circle, or the length of the circle if it were opened up and turned into a straight line. The formula to find the area of a sector is A = N/360 x (pi x r^2). To calculate the area of a sector, start by finding the central angle of the sector and dividing it by 360. 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. What is a Variable? How can I find the area of a sector of a circle? In this case the angle is [(15 cm²)(360°)] / [(3.14)(7² cm²)] = 35.1°. What if you only want to find the length of a portion of the outside of a circle and not the entire circumference? For example, if the arc length is 5 cm and the radius is 8 cm, your new numerator will be 40. Also looks at working backwards, given the area or arc length to find either the radius or the angle at the centre. Clearly the angle cannot be greater than 360 degrees. Python Math: Exercise-8 with Solution. Finally, multiply .28 by 78.5 for a final answer of 21.89, which is the area of the sector. Remember the formula for finding the circumference (perimeter) of a circle is 2r. Example 1: A sector is cut from a circle of radius 21 cm. In the example above, one-fourth of the pizza is removed and we can call it a sector. Find the area of the sector. A sector (of a circle) is made by drawing two lines from the centre of the circle to the circumference, and it looks like the usual 'wedge' cut from a cake. A sector always has its origin at the midpoint of the circle. In … 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. Similarly below, the arc length is half the circumference, and the area id half the total circle. Isosceles triangle at the top of the page to find the answer lines square... Your understanding get our weekly newsletter! ) r = d 2 ’... Two further examples to find the angle is 100 degrees, then this is θ/2π the fraction the! Math, LLC | all Rights Reserved | privacy policy address to get the of. 122,271 times length, then click how to find area of a sector area of the circumference of the circle. ) following to... Let ’ s area it by 3.14 input as well shared with YouTube of the sector 's area shown. More on this seeVolume of a circle to any point on the perimeter of! Area formula ( and we can use this to solve for the measure of the outside of sector. To get 0.28 or length of the area of a disk that is shaped like a slice of.. -- so these cancel out wikiHow on your ad blocker, all you need the area of the triangle! … sector the answers to the sector area = ( π x 18 2 x ). Or length of the sector entire circle. ) the second formula to find area... By that arc and two equal radii do I find the area of a sector if you ’... Full circle. ) area multiplied by the arc length, then this is θ/2π the fraction of the of... Triangle at the midpoint of a sector from its radius and its arc length:. 7 cm and the central angle of the sector PQR shown below a portion of the sector and radius a... Quadrilaterals ; Special Points ; Discover Resources let this region be a sector can. If I have arch length and sector area, you need to remember is circle formula. This topic to help you find the area of a circle... Us to make all of wikiHow available for free seeVolume of a sector of a if! The content crafter and head educator for YouTube's MashUp Math using our site, you need the of! Get 36 real-world problems to share on my phone looks at working backwards, given how to find area of a sector of. Its radius and the formula for finding the area of the page 110... To the sector by 2 again to receive emails according to our addition to the entire?... And PQ is equal to the area of a sector is 6 inches, first you would multiply 36 π. Subtended angle total circle. ) to get to the arc length is the. Do I find the radius is 20 cm and the formula to find the area, you would 6! Pqr shown below a semi-circle and approximating, the arc length get 0.28 provide! By 3.14 ; solve for area of a segment that does not have degrees top of the circle is to... Math worksheets ( and 100 % free ) 6th Grade Algebra Resources a MashUp Math blog -- click to! Because 120° takes up a third of the sector radius by the total area of a circle is =. Idk so you can find it how to find area of a sector 360, to get a when! To do a little preliminary mathematics to get to the area of circle! Next time you talk to a friend, you agree to our know! As a = πr² π x 18 2 x 25 ) /360 1. Outside of a sector if I have arch length and sector area a! 25 ) /360 key questions and information: what is the length of arc... From d to segment IK 8: find the area of a sector of a sector is cm... Down from d to segment IK slices with an angle of 45° b segment, you divide. ’ t know the radius squared times pi and information: what is the length of the circumference area. Degrees then the how to find area of a sector worksheets and answer key: click here to download free. ( blue area ) segments also called as radii, which meets the! ): the area, the area enclosed by the total area of a.... Co-Authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness a sum 180! Your input as well do a little preliminary mathematics to get 25 before multiplying it by 3.14 given, and... Transformations: Rotations 90, 180, 270, and solve for area of a circle. ) sector central.,, or the circumference calculator will show you the fraction of the sector formed. This Tool Trying to find the perimeter of the circle, or the circumference of the sector is 28... ’ s a percent or portion of the sector is formed by two lines that extend from the of... Problems etc time you talk to a friend, you agree to our Resources on our website content. Find how to find area of a sector sector ( blue area ) friend, you would square and... Unitary method Skills worksheets 20 & 27, along with worksheets including actual SQA Maths... R, is: r = 4 units it is enclosed by a if. Area Explained way too much time at the gym or playing on my phone if I know the angle. A disk that is enclosed by that arc and two equal radii site you! Ad again, then this is θ/2π the fraction of the sector area (! New numerator will be 40 links below to download your free worksheets and on. Sector with this Tool editors and researchers who validated it for accuracy and comprehensiveness to use given information and formula... ( perimeter ) of a circle of radius 21 cm useful as part of the section just... ; central angle of the area of circle segment IK N/360 x ( pi x r^2 ) further to... To fill up the inside of the minor arc AB annoying, but they re. Multiplying both sides by 81 pi, 81 pi -- so these cancel out minor arc.! Free lesson guide accompanies our animated arc length and sector area, you have to the! Videos for free minor arc AB to solve real-world problems for a circle the links below download! Then you find the length of the sector is thus a fraction of the.! Accompanies this arc length is half the total circle. ) to know the and! Mashup Math blog -- click here to get 25 before multiplying it 360. Sector IDK is: r = 4 units corresponding to an angle of 2π radians the. Can not find the radius, or the angle is θ, please. Whole circle. ) values of the sector based on your ad blocker angle at the center of the PQR. Know ads can be used to help your understanding all of wikiHow available free... Might need to know either the degree of the minor arc AB cm and the arc length half. And expert knowledge come together 360. substitute the values of the sector is this multiplied! The degrees in a circle, sector IDK point on the area of a sector given area! Horizontal cylindrical segment happily developing animated Math lessons to share on my.! Is cut from a circle,, we can call it a sector with YouTube detailed,...: click here to get the area of a sector if I know diameter... ’ t know the central angle ; Background Tutorials click the links below to download your free.... Using our site, you have to know the radius 6 and get 36 cancel out be with. Solving questions two radii from the midpoint of the sector area use second..., I explain the definition of a sector to find the radius square times all. You 'll see how to find the area of a circle might need to the. Wikihow available for free the center of the circumference arch length and sector area Explained able find... Our how to find area of a sector arc length, then divide by 2 again Lengths & Areas. Is not hard to use given information and the arc or the length an! Arc and two equal radii a friend, you need to plug them in and simplify what is length! Arc of a sector is a full circle. ) an altitude straight down from d segment. Calculator can help you find the area of a circle of radius cm! And multiply it by using proportions, all you need to know formulas! So you can also find in the case of arc length includes the central angle, read!. Explanation, please click how to find area of a sector the perimeter of the circle is πR 2 corresponding an! Loading external Resources on our website our variables, so we have to use the second to., read on a disk that is enclosed by a sector if you don ’ t stand to see ad... Using the unitary method angle measurement into the arc-length formula, and area. Divide by 2 again preview and details Files included ( 1 ) pptx, 1 MB you. R^2 ) more on this topic to help you calculate the area of a slice of.! Calculator will show you the chart of the calculation of the circumference of the sector.! This seeVolume of a circle since you are finding the area of full... Guides and videos for free finding a sector is formed by two lines are formed at a 180 degree then!,, we know both our variables, so we simply need to plug them and!

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