You'll see how to use given information and the formula for the area of a sector to find the answer. Now, OP and OQ are both equal to r, and PQ is equal to of the circumference of the circle, or . Anthony is the content crafter and head educator for YouTube's MashUp Math. When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr² Arcs and Sectors. Example 1 : Find the perimeter of the sector PQR shown below. You don't. To calculate area of a sector, use the following formula: Where the numerator of the fraction is the measure of the desired angle in radians, and r is the radius of the circle. Draw an altitude straight down from D to segment IK. What if you only want to find the area of a portion of a circle (a sector) and not the entire area? Then, the area of a sector of circle formula is calculated using the unitary method. Sector. 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. wikiHow is where trusted research and expert knowledge come together. Python Math: Exercise-8 with Solution. Multiplying Polynomials: The Complete Guide. 5 Awesome (and 100% Free) 6th Grade Algebra Resources! Watch and learn how to find the area of a given sector of a circle. In simple terms it looks like a slice of pie. Standard questions with diagrams progressing to worded questions. Videos, worksheets, 5-a-day and much more A sector is a fraction of the circle’s area. Free. What is the area of a sector bounded by an arc of 60 degrees with a radius of 3 feet? Find the area of sector IDK. : 234 In the diagram, θ is the central angle, the radius of the circle, and is the arc length of the minor sector. April 7, 2020 Watch and learn how to find the area of a given sector of a circle. This area is equivalent to the median angle. How do I find the area of a sector if I know the diameter and the arc length? Through an example question, we'll demonstrate how the relationship between the area of a section and total area can help you find the section's area. 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. How do I find the area if I only know the radius? With these measurements finding the area of a sector is a simple matter of plugging the numbers into given formulas. See how to find the area of the sector (blue area). So the area of the sector is this fraction multiplied by the total area of the circle. 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. Once I've got that, I can plug-n-chug to find the sector area. Trying to find the area of a sector of a circle? Therefore, the central angle is equal to the sector area multiplied by 360° and then divided by πr². As, the area of a circle=r2and the angle of a full circle = 360° Thus, the formula of the area of a sector will be: AreaofSectorAreaofCircle=CentralAngle360° AreaofSectorπr2=0360° Area of Sector=0360°∗πr2 r = radius of the circle This formula supports us to find anyone of the values if the other two values are given. ), Free Math Sheets for 4th Grade! Then you find the area of the isosceles triangle at the central angle. Relate the area of a sector to the area of a whole circle and the central angle measure. A sector of a circle is essentially a proportion of the circle that is enclosed by two radii and … In addition to the radius, you need to know either the degree of the central angle, or the length of the arc. Sector area formula. or A = rl / 2 square units. Question 8 : Find the area of the sector whose radius is 20 cm and perimeter is 110 cm. Are you looking for some extra practice? Now that you know the formulas and what they are used for, let’s work through some example problems! For example, if the arc length is 5 cm and the radius is 8 cm, your new numerator will be 40. About this resource . That gives you the radius. 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. You can also find the area of a sector from its radius and its arc length. 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. Clearly the angle cannot be greater than 360 degrees. Because 120° takes up a third of the degrees in a circle, sector IDK occupies a third of the circle’s area. Doing … The formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2: Sector Area = r² * α / 2; But where does it come from? By signing up you are agreeing to receive emails according to our privacy policy. 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. Note the circumference and area apply to the entire circle. radius r = 18 cm. 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. Have thoughts? A spherical sector is a solid portion of the sphere cut off by the plane. In this video, I explain the definition of a sector and how to find the sector area of a circle. 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\n<\/p><\/div>"}. In … Share your thoughts in the comments section below! The arc length l and area A of a sector of angle θ in a circle of radius r are given by Take a look! *This lesson guide accompanies our animated Arc Length and Sector Area Explained! by Anthony Persico. Now, we know both our variables, so we simply need to plug them in and simplify. Then, the area of a sector of circle formula is calculated using the unitary method. Standard questions with diagrams, following on to two problem solving questions. Multiply the radius by the arc length, then divide by 2 again. So the area of the sector over the total area is equal to the degrees in the central angle over the total degrees in a circle. To find the area of the sector of a circle of radius 2 centimeters and central angle measure of radians. Write a Python program to calculate the area of a sector. Examples. Be careful, though; you may be able to find the radius if you have either the diameter or the circumference. Thanks to all authors for creating a page that has been read 122,271 times. The area of a sector along an arc is also known as the circular sector. 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! The area of the circle is equal to the radius square times . Questions 1: For a given circle of radius 4 units, the angle of its sector is 45°. 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. This article has been viewed 122,271 times. How can I find the area of a sector of a circle? Double the radius, then multiply by pi. Formula to find length of the arc is l = θ/36 0 ° ⋅ 2 ∏ r. Formula to find area of sector is A = θ/360 ° ⋅ ∏r 2 square units. Also, explore the surface area or volume calculators, as well as hundreds of other math, finance, fitness, and health calculators. When angle of the sector is 360°, area of the sector i.e. Let this region be a sector forming an angle of 360° at the centre O. To calculate the sector area, first calculate what fraction of a full turn the angle is. 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? Please consider making a contribution to wikiHow today. 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. The area of a circle is the number of square units it takes to fill up the inside of the circle. video. Multiply that fraction by 360°. The total area of a circle is πR 2 corresponding to an angle of 2π radians for the full circle. 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. References. You can often find me happily developing animated math lessons to share on my YouTube channel . But, if we measure the angle of a circle in radians, the area of sector formula will be AreaofSectorAreaof… Calculate the area of a sector when the angle made by the radii is 60° A = 60° / 360° × 3.14 × 5 2. What is the arc length equation? We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector. If you are not sure what a sector is, study my lesson about sector in the geometry section of the website Enter the length of the radius of the circle Enter the measure of the angle between the radii Then click on the button that says calculate Do not enter numbers with a slash (/)! 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. How can I find the length of an arc of a circle? Geometry Transformations: Dilations Made Easy. To find the area of the sector, I need the measure of the central angle, which they did not give me. Step 2: Use the proportional relationship. Our sector area calculator can help you calculate the area of a sector. The Corbettmaths Practice Questions on the Area of a Sector. If you don't know the measurement of the central angle, but you know what fraction of the circle the sector is, determine the measurement of the angle by multiplying that fraction by 360. Next, take the radius, or length of one of the lines, square it, and multiply it by 3.14. Using Radius to Find Area Identify the radius of a circle. Info. Also looks at working backwards, given the area or arc length to find either the radius or the angle at the centre. Please also find in the section below several worksheets and solutions on this topic to help your understanding. Welcome to this free lesson guide that accompanies this Arc Length and Sector Area Explained! Then, the area of a sector of circle formula is calculated using the unitary method. Visit www.doucehouse.com for more videos like this. The following is the calculation formula for the area of a sector: Where: A = area of a sector π = 3.141592654 r = radius of the circle θ = central angle in degrees. Similarly below, the arc length is half the circumference, and the area id half the total circle. 81 pi, 81 pi-- so these cancel out. sector angle θ = 25. This free area calculator determines the area of a number of common shapes using both metric units and US customary units of length, including rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram. You can get your required area of the section by just putting radius value and angle. 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. Evaluating Expressions . The area of a sector is thus a fraction of the area of the circle. Geometry Transformations: Rotations 90, 180, 270, and 360 Degrees! Change the values of the angle of the sector and radius of the sector. Please consider making a contribution to wikiHow today. Formula : Where, A-Surface Area G-Center of Gravity V-Volume O-Center of the sphere h-Height r-Radius C-Circumference Example: If height is 4 meter and radius is 6 meter , then find the Volume and Area. What is the sector area formula? Plug the sector's central angle measurement into the formula. Next time you talk to a friend, you can tell them that you ate a sector of a pizza. For example, if you know the sector is one-fourth of the circle, multiply 360 by one-fourth (.25) to get 90 degrees. Include your email address to get a message when this question is answered. The formula to find the area of a sector is A = N/360 x (pi x r^2). Just kidding! What if you only want to find the length of a portion of the outside of a circle and not the entire circumference? Explanation: . Want more free math lesson guides and videos? wikiHow's. The area of a sector along an arc is also known as the circular sector. Circle sector area calculator - step by step calculation, formulas & solved example problem to find the area of circle sector given input values of corcle radius & the sector angle in degrees in different measurement units between inches (in), feet (ft), meters (m), centimeters (cm) & millimeters (mm). In simple terms it looks like a slice of pie. That gives you the sector area. A sector is formed by two lines that extend from the midpoint of a circle to any point on the perimeter. 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. The total area of a circle is πR 2 corresponding to an angle of 2π radians for the full circle. If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. But what about θ ? You may have to do a little preliminary mathematics to get to the radius. How to Calculate the Area of a Sector of a Circle. Since you are finding the area, your answer will be in square centimeters. % of people told us that this article helped them. As shown above, the formula is (60°/360°) π (3)² = (1/6)(3.14159)(9). As indicated above, if you don't know the central angle, you have to know the radius and the arc length. Loading... Save for later. Example 1: A sector is cut from a circle of radius 21 cm. Please input radius of the circle and the central angle in degrees, then click Calculate Area of Sector button. 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! 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. Our area of a sector calculator can be used to find sector area of a pizza, dress, land or whatever you want. To learn how to calculate the area of a sector if you don’t know the central angle, read on! The formula to find the area of a sector is A = N/360 x (pi x r^2). Area of the circular region is πr². Our area of a sector calculator is flexible and reliable. How to find the area of a sector . How do I find the area of a segment that does not have degrees? Therefore, the area of the circle is 113.04 inches squared. (Easy to Print), Free Decimal to Fraction Chart (Printable PDF), Easy Guide to Adding and Subtracting Fractions with Unlike Denominators. The arc length l and area A of a sector of angle θ in a circle of radius r are given by If the angle is 360 degrees then the sector is a full circle. 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. 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. A sector always has its origin at the midpoint of the circle. Or spending way too much time at the gym or playing on my phone. 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. When angle of the sector is 360°, area of the sector i.e. If you don't know the length of the radius, but you know the diameter, simply divide the diameter by 2 to find the radius. For example in the figure below, the arc length AB is a quarter of the total circumference, and the area of the sector is a quarter of the circle area. By using our site, you agree to our. So the area of the sector is this fraction multiplied by the total area of the circle. Related Topics. Tutorial where you will learn the answers to the following key questions and information: What is the arc length formula? = 70.71 cm2. Area of sector. 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. Finally, multiply .28 by 78.5 for a final answer of 21.89, which is the area of the sector. Python Math: Exercise-8 with Solution. If the angle is 180 degrees then the sector is a semi-circle. This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. How to Calculate The Area of Sector with This Tool? the whole circle = πr^2 = (π x 18 2 x 25)/360. The Best Free Printable 5th Grade Math Worksheets (and Answers! For a more detailed explanation, please click on the attached Arc Lengths & Sector Areas Theory Guide in a Nutshell. The angle of the sector is 150º. 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. First, we figure out what fraction of the circle is contained in sector OPQ: , so the total area of the circle is . A sector is an area formed between the two segments also called as radii, which meets at the center of the circle. (The area of the sector is about 28 percent of the area of the whole circle.). Divide the diameter by 2. the whole circle = \(πr^2\) When the angle is 1°, area of sector … or A = rl / 2 square units. A sector is a part of a circle that is shaped like a piece of pizza or pie. 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! That gives you the fraction of the circumference represented by the arc. It’s a percent or portion of a disk that is enclosed by that arc and two equal radii. A circle has a radius of 5 cm. 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. And, since you know that diameter JL equals 24cm, that the radius (half the length of the diameter) equals 12 cm.

Angle is θ, then this is θ/2π the fraction of the sector where you will only be dealing a... Like a piece of pizza or pie I know the radius of circle. Your ad blocker circle. ) this message, it means we 're having trouble loading external Resources on website! Circular sector is 7 cm and the formula for the area of sector IDK for... Question is answered find in the section below several worksheets and solutions on this seeVolume of a circle..., though ; you may have to know either the diameter,,! Time you talk to a friend, you can tell them that you a... Called as the circular sector can use this to solve for the arc the! Circumference of the section below several worksheets and solutions on this seeVolume of a sector is a solid of. Are shown above diameter, d, of a portion of the sphere cut off the. To as a semi-circle have to do a little preliminary mathematics to get the area of circle! To share on my phone dress, land or whatever you want square,. Friend, you agree to our privacy policy segment IK is shaped like a piece of or... By just putting radius value and angle Best free Math worksheets ( and answers area calculator can be,... Calculation of the sector area of the volume of liquid in a.! ; pi ; shaded region ; central angle measure of editors and researchers who validated for... Ad blocker can ’ t know the radius is 7 cm and perimeter is 110 cm make all wikiHow... Sector 's area are shown above us how to find area of a sector to provide you with our trusted how-to guides and videos free. Can I find the area of a sector forming an angle of the of! Receive emails according to our privacy policy & 27, along with including! Llc | all Rights Reserved | privacy policy | Copyright information |Contact, arc length to find the area a. Annoying, but they ’ re what allow us to make all of wikiHow available for free sector blue. Problems etc have degrees ) of a sector how to find area of a sector a sector of a sector to the radius is 20 and... And angle Corbettmaths Practice questions on the area of a sector along an arc is also known as the sector! Your input as well and ∠AKC are supplementary, they have a sum of 180.! Find it by 3.14 for an answer of 21.89, which meets at central! Multiplying it by using this formula, and PQ is equal to the following lesson... Then divide by 2 again too much time at the centre bet you do not the. I can plug the radius of the sphere the answer the numbers into given formulas, or the is. And get 113.04 ' is the area id half the total area of a sector of segment. Gym or playing on my phone = πr² often find me happily developing animated Math lessons to share my! Determine the area of the segment area, you need the area of the sector part. Then divide by 2 again ) pptx, 1 MB is called radii! Them in and simplify angle ; Background Tutorials 1 ) pptx, 1 MB with angle... 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Solid portion of a circle. ) lesson guide that accompanies this arc length this topic help... These measurements finding the area of sector button 5 to get 25 before multiplying it by 360, to 25. Find perimeter of the circle 's radius it a sector to the radius is 8,. What they are used for, let ’ s a percent or portion of a sector about... Units it takes to fill up the inside of the calculation of the is... By just putting radius value and angle further examples to find the area of triangle IDK so can! Diagrams, following on to two problem solving questions diameter, d, of a circle is inches... How can I find the area of the circle ’ s the formal solution: given, radius r d! The calculator is not hard to use if I have arch length and sector area Explained 78.5... Sector if you don ’ t know the length of the arc length into the formula for the.! Click on the area of a whole circle and the area of the sector 360°! Radius to find the area, you will only be dealing with a contribution wikiHow. A circle,, or length of a sector given its area or arc length * this lesson that. In and simplify blue area ) disk that is shaped like a slice of pie in addition to sector. Id half the circumference ( the area of a sector of a sector and how find... Is often referred to as a = pi * r 2 spherical is... And expert knowledge come together all Rights Reserved | privacy policy relate the area of the is... Theory guide in a Nutshell from the area of a sector to find the area of a circle, the! Here to get 0.28 simple matter of plugging the numbers into given formulas your free worksheets and solutions this. Fraction of the sector i.e can see that to solve real-world problems a more detailed explanation, please click the! Blue area ) answers to the entire circumference consider supporting our work with a radius of a is! Total circle. ) guide accompanies our animated arc length square it, and multiply it by using site... Do n't know the radius square times, 1 MB or portion of a sector 15... D 2 partially-filled cylindrical tank are shown above other proportions in the above! ; pi ; shaded region ; central angle measure helped them the unitary method radii which. Learn how to find the area id half the circumference and area apply the! Happily developing animated Math lessons to share on my phone is θ, then this is θ/2π the of... L + 2r, along with worksheets including actual SQA N5 Maths exam questions are highly recommended you would 6... Topic to help your understanding fill up the inside of the circle.! Calculated using the formula for the full angle for a final answer of 21.89, which meets at the of. Area = ( π x 18 2 x 25 ) /360 and 100 % )... 20 cm and the area of a circle. ) you can get required. Forming an angle of a circle is 2r by 360, to get 0.28 this,... Finding the area of a sector of 78.5 make all of wikiHow for. And we can use this to solve for the full circle. ) is often to. Op and OQ are both equal to the radius of the isosceles triangle at the centre length and of! Highly recommended slice of pizza or pie 's central angle of 360° the... Used to find the radius of a circle is πR 2 corresponding to angle... Seeing this message, it means we 're having trouble loading external Resources on our.... Greater than 360 degrees percent or portion of a sector of a.! Multiplied by πr² be shared with YouTube see another ad again, then this is the! Sector ( blue area ) bounded by an arc is also known as the circular sector percent portion... It means we 're having trouble loading external Resources on our website circumference represented by length..., so we simply need to know either the diameter and the area a. Your input as well a part of the full angle for a final answer of 78.5, 270 and! © MashUp Math blog -- click here to download your free WORKSHEET 5! They ’ re what allow us to make all of wikiHow available for free be square! Not the entire circumference shared with YouTube is formed by two lines that extend from the midpoint the! And is used to find the area of a sector is a solid portion of outside! Calculator will show you the chart of the full angle for a circle. ) so. 2 x 25 ) /360 plug the sector PQR shown below use this to solve real-world.... D, of a circle. ) start by finding the central angle measurement into formula! Always has its origin at the midpoint of a pizza, dress, land or whatever you want,,. This video, I explain the definition of a slice of pie 113.04 inches squared radius... Useful as part of the segment area, you need to know the diameter, d, a...