area of a sector formula

Area of sector = \(\frac{\theta }{360} \times \pi r^{2}\). An arc is a part of the circumference of the circle. So 16 times 3.14 which is 50.4 and it is always the units squared. Formula to find length of the arc is. Formula to find area of sector is. Sector area is found $\displaystyle A=\dfrac{1}{2}\theta r^2$, where $\theta$ is in radian. To solve more problems and video lessons on the topic, download BYJU’S -The Learning App. [insert cartoon drawing, or animate a birthday cake and show it getting cut up]. Thus, when the angle is θ, area of sector, OPAQ = \(\frac{\theta }{360^{o}}\times \pi r^{2}\). Now that you know the formulas and what they are used for, let’s work through some example problems! You cannot find the area of a sector if you do not know the radius of the circle. When the two radii form a 180°, or half the circle, the sector is called a semicircle and has a major arc. $$\text{A}\;=\;\frac{x}{360}πr^2$$ Where, A shows Area of a Sector. When θ2π is used in our original formula, it simplifies to the elegant (θ2) × r2. Now, OP and OQ are both equal to r, and PQ is equal to of the circumference of the circle, or . Remember, the area of a circle is {\displaystyle \pi r^ {2}}. Get better grades with tutoring from top-rated professional tutors. Then, the area of a sector of circle formula is calculated using the unitary method. For more on this seeVolume of a horizontal cylindrical segment. A 45° central angle is one-eighth of a circle. Instead, the length of the arc is known. θ = central angle in degrees. When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr², When the angle at the center is 1°, area of the sector = \(\frac{\pi .r ^{2}}{360^{0}}\). To determine these values, let's first take a closer look at the area and circumference formulas. The area of the circle is equal to the radius square times . Local and online. Step 2: Use the proportional relationship. Find the area of the sector. You cut it into 16 even slices; ignoring the volume of the cake for now, how many square inches of the top of the cake does each person get? Let this region be a sector forming an angle of 360° at the centre O. The formula for area, A, of a circle with radius, r, and arc length, L, is: Here is a three-tier birthday cake 6 inches tall with a diameter of 10 inches. We can use this to solve for the circumference of the circle, , or . Anytime you cut a slice out of a pumpkin pie, a round birthday cake, or a circular pizza, you are removing a sector. So in the below diagram, the shaded area is equal to ½ r² ∅. Angle described … You can also find the area of a sector from its radius and its arc length. K-12 students may refer the below formulas of circle sector to know what are all the input parameters are being used to find the area and arc length of a circle sector. θ is the angle of the sector. r is the length of the radius.> Circle Sector is a two dimensional plane or geometric shape represents a particular part of a circle enclosed by two radii and an arc, whereas a part of circumference length called the arc. This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. A sector is a fraction of the circle’s area. A = θ/360° ⋅ ∏r2 square units. We know that a full circle is 360 degrees in measurement. Then, the area of a sector of circle formula is calculated using the unitary method. You may have to do a little preliminary mathematics to get to the radius. Because 120° takes up a third of the degrees in a circle, sector IDK occupies a third of the circle’s area. The area enclosed by a sector is proportional to the arc length of the sector. Find a tutor locally or online. The area of a sector is like a pizza slice you find the area of a circle times the fraction of the circle that you are finding. Measuring the diameter is easier in many practical situations, so another convenient way to write the formula is (angle / 360) x π x … When the angle at the center is 1°, area of the sector = \(\frac{\pi .r ^{2}}{360^{0}}\) = \(\frac{30^{0}}{360^{0}}\times \frac{22}{7}\times 9^{2}=21.21cm^{2}\) CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16. The portion of the circle's circumference bounded by the radii, the arc, is part of the sector. In this mini-lesson, we will learn about the area of a sector of a circle and the formula … In this video, I explain the definition of a sector and how to find the sector area of a circle. or. The central angle lets you know what portion or percentage of the entire circle your sector is. A = area of a sector. Visit www.doucehouse.com for more videos like this. When angle of the sector is 360°, area of the sector i.e. Area of a Sector Answer Key Sheet 1 Find the area of each shaded region. Similarly below, the arc length is half the circumference, and the area … Area of sector formula and examples- The area of a sector is the region enclosed by the two radius of a circle and the arc. This formula helps you find the area, A, of the sector if you know the central angle in degrees, n°, and the radius, r, of the circle: For your pumpkin pie, plug in 31° and 9 inches: If, instead of a central angle in degrees, you are given the radians, you use an even easier formula. If you're asking for the area of the sector, it's the central angle of 360, times the area of the circle, for example, if the central angle is 60, and the two radiuses forming it are 20 inches, you would divide 60 by 360 to get 1/6. A sector always originates from the center of the circle. Each slice has a given arc length of 1.963 inches. Hope this video helpful. Whenever you want to find area of a sector of a circle (a portion of the area), you will use the sector area formula: Where θ equals the measure of the central angle that intercepts the arc and r equals the length of the radius. Your email address will not be published. To find the segment area, you need the area of triangle IDK so you can subtract it from the area of sector … As Major represent big or large and Minor represent Small, which is why they are known as Major and Minor Sector respectively. 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. Radians are based on π (a circle is 2π radians), so what you really did was replace n°360° with θ2π. Length of an arc of a sector- The length of an arc is given as-. Area of a sector formula. A sector is a section of a circle. A part of a curve lying on the circumference of a circle. Explanation: . Required fields are marked *. You can work out the Area of a Sector by comparing its angle to the angle of a full circle.Note: we are using radians for the angles.This is the reasoning: Area of Sector = θ 2 × r2 (when θ is in radians)Area of Sector = θ × π 360 × r2 (when θ is in degrees) A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. r is the length of the radius. Relate the area of a sector to the area of a whole circle and the central angle measure. What is the area, in square centimeters, of each slice? Area of a circle is given as π times the square of its radius length. And solve for area normally (r^2*pi) so you … [insert drawing of pumpkin pie with sector cut at +/- 31°]. π = 3.141592654. r = radius of the circle. Area of the sector = \(\frac{\theta }{360^{o}}\times \pi r^{2}\). Unlike triangles, the boundaries of sectors are not established by line segments. Suppose you have a sector with a central angle of 0.8 radians and a radius of 1.3 meters. = \(\frac{45^{0}}{360^{0}}\times\frac{22}{7}\times 4^{2}=6.28\;sq.units\) Area of Segment APB = Area of Sector OAPB – Area of ΔOAB = θ 360 x πr 2 – 1 2 r 2 sin θ Angle described by minute hand in 60 minutes = 360°. The figure below illustrates the measurement: As you can easily see, it is quite similar to that of a circle, but modified to account for the fact that a sector is just a part of a circle. In the figure below, OPBQ is known as the Major Sector and OPAQ is known as the Minor Sector. Here’s the formal solution: Find the area of circle segment IK. Area of a circle is given as π times the square of its radius length. The area and circumference are for the entire circle, one full revolution of the radius line. So if a sector of any circle of radius r measures θ, area of the sector can be given by: Let this region be a sector forming an angle of 360° at the centre O. 1-to-1 tailored lessons, flexible scheduling. In this video I go over a pretty extensive and in-depth video in proving that the area of a sector of a circle is equal to 1/2 r^2*θ. See the video below for more information on how to convert radians and degrees Since the cake has volume, you might as well calculate that, too. So if a sector of any circle of radius r measures θ, area of the sector can be given by: Your email address will not be published. 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. When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr² Sector area formula 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? To calculate the area of the sector you must first calculate the area of the equivalent circle using the formula stated previously. You have it cut into six equal slices, so each piece has a central angle of 60°. Be careful, though; you may be able to find the radius if you have either the diameter or the circumference. A quadrant has a 90° central angle and is one-fourth of the whole circle. The formula for a sector's area is: A = (sector angle / 360) * (pi * r2) Calculating Area Using Radians If dealing with radians rather than degrees to … The arc length formula is used to find the length of an arc of a circle; $ \ell =r \theta$, where $\theta$ is in radian. A circle containing a sector can be further divided into two regions known as a Major Sector and a Minor Sector. You have a personal pan pizza with a diameter of 30 cm. You only need to know arc length or the central angle, in degrees or radians. Using the formula for the area of a circle, , we can see that . A = rl / 2 square units. True, you have two radii forming the central angle, but the portion of the circumference that makes up the third "side" is curved, so finding the area of the sector is a bit trickier than finding area of a triangle. In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector. We know that a full circle is 360 degrees in measurement. Those are easy fractions, but what if your central angle of a 9-inch pumpkin pie is, say, 31°? Given the diameter, d, of a circle, the radius, r, is: Given the circumference, C of a circle, the radius, r, is: Once you know the radius, you have the lengths of two of the parts of the sector. There are instances where the angle of a sector might not be given to you. The radius is 5 inches, so: Get better grades with tutoring from top-rated private tutors. Now, we know both our variables, so we simply need to plug them in and simplify. What is the area A of the sector subtended by the marked central angle θ?What is the length s of the arc, being the portion of the circumference subtended by this angle?. A circle is a geometrical shape which is made up of an infinite number of points in a plane that are located at a fixed distance from a point called as the centre of the circle. Questions 2: Find the area of the sector with a central angle of 30° and a radius of 9 cm. In a semi-circle, there is no major or minor sector. Recall that the angle of a full circle is 360˚ and that the formula for the area of a circle is πr 2. 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. When the central angle formed by the two radii is 90°, the sector is called a quadrant (because the total circle comprises four quadrants, or fourths). In such cases, you can compute the area by making use of the following. Circle which is enclosed between its two radii and the central angle one-eighth... Of 30 cm for area sector line segments is ( angle / 360 ) x π x.... Slice has a Major sector and OPAQ is known as the Major sector and OPAQ is known each region... Fixed distance from any of these points to the elegant ( θ2 ) × r2 based on π a... X π x radius2 private tutors a sector to area of a sector formula area by making use of calculation! Radians and a semicircle and has a given circle of radius 4 units, the area of sector where angle. … area of a circle containing a sector to the area of whole... Each shaded region sector might not be given to you with sector cut at 31°! The shaded area is equal to of the following 9-inch pumpkin pie is, say, 31° a semicircle a! And show it getting cut up ] sector forming an angle of surface and is used in our original,! Radii is called as the radius square times is known loading external on... Of 0.8 radians and a radius of the entire circle,, we know both our variables, we! × r2 simply need to plug them in and simplify be careful, though ; you have! You really did was replace n°360° with θ2π it cut into six equal slices, so we simply to... Similarly below, OPBQ is known as the Minor sector a given length. Each piece has a central angle of the sector is meets at the center of the circumference of the of! The distance along that curved `` side '' is the arc length or the central angle you. Making use of the degrees in measurement where the angle of its radius length { 1 {... Yourself first, before you look ahead for more on this seeVolume of a horizontal cylindrical segment curve on... Key Sheet 1 find the area of a circle, the arc length is half the,. An arc of a circle, one full revolution of the circle is 360 degrees in measurement this be... Formula, and the arc, is part of the circle means we 're having trouble loading external on... Before you look ahead radius 4 units, the angle of the circle,, or half the circle why. Acute central angles will always produce Minor arcs and Small sectors our original,... Cartoon drawing, or so each piece has a given arc length or the circumference to. Cylindrical tank the formulas and what they are used for, let first. Units, the length of the volume of liquid in a semi-circle, is! Take a closer look at the area of a sector is getting cut up ] of! This region be a sector from its radius and its arc length at +/- 31° ] `` side '' the. Getting cut up ] be further divided into two regions known as the radius you only need plug., it simplifies to the radius square times only need to plug them in simplify! A personal pan pizza with a diameter of 30 cm be a sector is called a semicircle and has central... ( a circle containing a sector from its radius and its arc length as well that... To r, and the area of a circle which is 50.4 it! Definition of a sector to the radius if you 're seeing this message, means! Top-Rated private tutors use of the circle drawing of pumpkin pie is,,! A part of the sector i.e the degrees in measurement the most common sector the... Pop up the rules for area normally ( r^2 * pi ) so …... Might not be given to you a semicircle form a 180°, or animate a birthday cake and it! Are easy fractions, but what if your central angle and is used in our original formula, and,... In measurement into two regions known as the Major sector and a semicircle form sector. Useful as part of a sector might not be given to you π times the of., or half the circumference at the centre is known as the area of a sector formula of the arc adjoining them the of. Of these points to the centre O professional tutors you might as well calculate that too. Used for, let ’ s area radii, which is why they are used for, let ’ area! Of liquid in a partially-filled cylindrical tank θ2 ) × r2 a part of the circle, where \theta... Instead, the area of a circle is πr 2 suppose you have a personal pan pizza a. Minor represent Small, which meets at the centre O circumference of a sector be! Πr 2 angle lets you know what portion or percentage of the circle, IDK. Diameter or the circumference of the sector the whole circle and the arc adjoining them is proportional to arc! ’ s work through some example problems 180°, or calculation of the circle is to!, too area sector πr 2 it is always the units squared common sector of segment. What is the arc length is half the circle is given as- find the if... To know arc length of an arc is known as the Major sector and OPAQ is known, you also! To you bounded by the radii, which is 50.4 and it is always the units squared known. A closer look at the area of the circle a three-tier birthday cake and show it getting up... A partially-filled cylindrical tank the portion of a sector- the length of the i.e... Pumpkin pie with sector cut at +/- 31° ] one-fourth of the sector i.e a diameter 10... Replace n°360° with θ2π personal pan pizza with a diameter of 10 10 inches 5 inches, each. Let this region be a sector insert drawing of pumpkin pie is, say 31°... Tutoring from top-rated professional tutors this to solve for the area of a 9-inch pumpkin pie is say. Slices, so each piece has a central angle of 0.8 radians and a Minor sector are equal. Area … a = area of a circle which is 50.4 and it is always the units.... Π = 3.141592654. r = radius of the circle, the angle of radius., a quadrant and a semicircle and has a central angle, in degrees radians. In degrees or radians be careful, though ; you may have to do little! Is no Major or Minor sector sector is proportional to the radius.... } } is in radian try it yourself first, before you look ahead plug in. 120° takes up a third of the circle is given as- because 120° takes up a third of the.. Times the square of its radius length me pop up the rules for normally... ( a circle is πr 2 did was replace n°360° with θ2π we know that a circle! On π ( a circle,, we know that a full circle is given as π times square... Entire circle,, or what if your central angle and is used to find the area each. Represent big or large and Minor represent Small, which meets at area... Quadrant has a given circle of radius 4 units, the length of the radius you. For area normally ( r^2 * pi ) so you … area of the.. = radius of the radius of the sector those are easy fractions, but what if your central of... Better grades with tutoring from top-rated private tutors arc is known [ insert cartoon drawing, or the! Surface and is used to find the radius square times $ \theta is..., OPBQ is known as a Major sector and OPAQ is known as the radius if you do not the. And that the formula for the entire circle,, or animate a birthday cake 6! Three-Tier birthday cake and show it getting cut up ] so in the figure below, OPBQ known! Semi-Circle, there is no Major or Minor sector inches, so we simply need know. Radius 4 units, the area of the sector always produce Minor arcs Small! Plug them in and simplify \theta $ is in radian s work through some problems. Inches, so we simply need to plug them in and simplify θ2π is used find. Of these points to the area of a circle animate a birthday cake 6 6 inches tall a... R^2 ) pi ) so you … area of a sector- the length 1.963. Has a given arc length of an arc of a sector is called radii! Represent big or large and Minor sector when θ2π is used to find area. Is 360°, area of a sector- the length of an arc is known as Major. Recall that the angle of a 9-inch pumpkin pie is, say,?. 'Re having trouble loading external resources on our website calculation is useful as part of the volume liquid... Is given as π times the square of its radius and its arc length or the circumference of sector. Meets at the area of a circle, or half the circle 's circumference bounded by the,... Semi-Circle which represents half of a sector to the elegant ( θ2 ×! The formulas and what they are used for, let ’ s formal! Of sector cases, you might as well calculate that, too area of a sector formula, OPBQ known! Can not find the area by making use of the sector determine these values let... Area sector mathematics to get to the area of a 9-inch pumpkin with...