# area of a sector formula

Angle described … When the angle at the centre is 360°, area of the sector, i.e., the complete circle = πr² Area of a sector formula. 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°. 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 this video, I explain the definition of a sector and how to find the sector area of a circle. Relate the area of a sector to the area of a whole circle and the central angle measure. A quadrant has a 90° central angle and is one-fourth of the whole circle. Let this region be a sector forming an angle of 360° at the centre O. A circle containing a sector can be further divided into two regions known as a Major Sector and a Minor Sector. A = area of a sector. Your email address will not be published. r is the length of the radius.> The most common sector of a circle is a semi-circle which represents half of a circle. If you're seeing this message, it means we're having trouble loading external resources on our website. To calculate the area of the sector you must first calculate the area of the equivalent circle using the formula stated previously. Anytime you cut a slice out of a pumpkin pie, a round birthday cake, or a circular pizza, you are removing a sector. Here’s the formal solution: Find the area of circle segment IK. So if a sector of any circle of radius r measures θ, area of the sector can be given by: Local and online. The area and circumference are for the entire circle, one full revolution of the radius line. 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) See the video below for more information on how to convert radians and degrees Instead, the length of the arc is known. 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 … Acute central angles will always produce minor arcs and small sectors. 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. = $$\frac{30^{0}}{360^{0}}\times \frac{22}{7}\times 9^{2}=21.21cm^{2}$$ Thus, when the angle is θ, area of sector, = $$\frac{\theta }{360^{o}}\times \pi r^{2}$$, = $$\frac{45^{0}}{360^{0}}\times\frac{22}{7}\times 4^{2}=6.28\;sq.units$$, = $$\frac{30^{0}}{360^{0}}\times \frac{22}{7}\times 9^{2}=21.21cm^{2}$$, video lessons on the topic, download BYJU’S -The Learning App. Using the formula for the area of a circle, , we can see that . You have it cut into six equal slices, so each piece has a central angle of 60°. = $$\frac{45^{0}}{360^{0}}\times\frac{22}{7}\times 4^{2}=6.28\;sq.units$$ Let me pop up the rules for area sector. The fixed distance from any of these points to the centre is known as the radius of the circle. A = rl / 2 square units. [insert cartoon drawing, or animate a birthday cake and show it getting cut up]. Area of a circle is given as π times the square of its radius length. You may have to do a little preliminary mathematics to get to the radius. Area of the sector = $$\frac{\theta }{360^{o}}\times \pi r^{2}$$. 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. The radius is 5 inches, so: Get better grades with tutoring from top-rated private tutors. Questions 2: Find the area of the sector with a central angle of 30° and a radius of 9 cm. Find the area of the sector. Learn faster with a math tutor. Area of a circle is given as π times the square of its radius length. 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. Area of Sector The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle. A sector is created by the central angle formed with two radii, and it includes the area inside the circle from that center point to the circle itself. Relate the area of a sector to the area of a whole circle and the central angle measure. In this mini-lesson, we will learn about the area of a sector of a circle and the formula … Recall that the angle of a full circle is 360˚ and that the formula for the area of a circle is πr 2. Then, the area of a sector of circle formula is calculated using the unitary method. The central angle lets you know what portion or percentage of the entire circle your sector is. Remember, the area of a circle is {\displaystyle \pi r^ {2}}. Get better grades with tutoring from top-rated professional tutors. In such cases, you can compute the area by making use of the following. 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Area of sector. Try it yourself first, before you look ahead! Each slice has a given arc length of 1.963 inches. And solve for area normally (r^2*pi) so you … Because 120° takes up a third of the degrees in a circle, sector IDK occupies a third of the circle’s area. Suppose you have a sector with a central angle of 0.8 radians and a radius of 1.3 meters. 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. A = θ/360° ⋅ ∏r2 square units. 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. Visit www.doucehouse.com for more videos like this. 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. Want to see the math tutors near you? Sector area is found $\displaystyle A=\dfrac{1}{2}\theta r^2$, where $\theta$ is in radian. To find Area, A, of a sector with a central angle θ radians and a radius, r: Our beloved π seems to have disappeared! The portion of the circle's circumference bounded by the radii, the arc, is part of the sector. 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. r is the length of the radius. Area of the sector = $$\frac{\theta }{360^{0}}\times \pi r^{2}$$. 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. It hasn't, really. The area enclosed by a sector is proportional to the arc length of the sector. In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector. There are instances where the angle of a sector might not be given to you. You cannot find the area of a sector if you do not know the radius of the circle. The formula to calculate the sector area is: \ (\text {Sector area} = \frac {\text {angle}} {360} \times \pi r^2 \) Then, you must multiply that area by the ratio of the angles which would be theta/360 since the circle is 360, and theta is the angle of the sector. Questions 1: For a given circle of radius 4 units, the angle of its sector is 45°. 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. Required fields are marked *. 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. In the figure below, OPBQ is known as the Major Sector and OPAQ is known as the Minor Sector. So 16 times 3.14 which is 50.4 and it is always the units squared. Be careful, though; you may be able to find the radius if you have either the diameter or the circumference. x is the angle of the sector. Area of a Sector Formula : $$\text{A}\;=\;\frac{1}{2}θr^2$$ Where, A shows Area of a Sector. We can use this to solve for the circumference of the circle, , or . Area of sector = $$\frac{\theta }{360} \times \pi r^{2}$$ Derivation: In a circle with centre O and radius r, let OPAQ be a sector and θ (in degrees) be the angle of the sector. First, we figure out what fraction of the circle is contained in sector OPQ: , so the total area of the circle is . When finding the area of a sector, you are really just calculating the area of the whole circle, and then multiplying by the fraction of the circle the sector represents. When the angle at the center is 1°, area of the sector = $$\frac{\pi .r ^{2}}{360^{0}}$$ Those are easy fractions, but what if your central angle of a 9-inch pumpkin pie is, say, 31°? 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. 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?. So in the below diagram, the shaded area is equal to ½ r² ∅. 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. Round the answer to two decimal places. 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? Here is a three-tier birthday cake 6 6 inches tall with a diameter of 10 10 inches. When the two radii form a 180°, or half the circle, the sector is called a semicircle and has a major arc. A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. An arc is a part of the circumference of the circle. θ is the angle of the sector. As Major represent big or large and Minor represent Small, which is why they are known as Major and Minor Sector respectively. The angle between the two radii is called as the angle of surface and is used to find the radius of the sector. A 45° central angle is one-eighth of a circle. For more on this seeVolume of a horizontal cylindrical segment. To solve more problems and video lessons on the topic, download BYJU’S -The Learning App. Hope this video helpful. Explanation: . When θ2π is used in our original formula, it simplifies to the elegant (θ2) × r2. 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. You have a personal pan pizza with a diameter of 30 cm. 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. A sector is a fraction of the circle’s area. Formula A sector is an area formed between the two segments also called as radii, which meets at the center of the circle. When angle of the sector is 360°, area of the sector i.e. Formula For Area Of Sector (In Degrees) We will now look at the formula for the area of a sector where the central angle is measured in degrees. To find the segment area, you need the area of triangle IDK so you can subtract it from the area of sector … Length of an arc of a sector- The length of an arc is given as-. Area of sector = $$\frac{\theta }{360} \times \pi r^{2}$$. In a semi-circle, there is no major or minor sector. Now, OP and OQ are both equal to r, and PQ is equal to of 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 … l = θ/360° ⋅ 2∏r. Then, the area of a sector of circle formula is calculated using the unitary method. Formula to find area of sector is. Area of a Sector Answer Key Sheet 1 Find the area of each shaded region. Your formula is: You can also find the area of a sector from its radius and its arc length. Similarly below, the arc length is half the circumference, and the area … Get help fast. The area of the circle is equal to the radius square times . [insert drawing of pumpkin pie with sector cut at +/- 31°]. Radians are based on π (a circle is 2π radians), so what you really did was replace n°360° with θ2π. Find a tutor locally or online. What is the area, in square centimeters, of each slice? or. You can also find the area of a sector from its radius and its arc length. This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. We know that a full circle is 360 degrees in measurement. 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. Using this formula, and approximating , the area of the circle is . π = 3.141592654. r = radius of the circle. 1-to-1 tailored lessons, flexible scheduling. Formula to find length of the arc is. 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. The formula for the area of a sector is (angle / 360) x π x radius2. A  part of a curve lying on the circumference of a circle. 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. You only need to know arc length or the central angle, in degrees or radians. In a semi-circle, there is no major or minor sector. Unlike triangles, the boundaries of sectors are not established by line segments. $$\text{A}\;=\;\frac{x}{360}πr^2$$ Where, A shows Area of a Sector. In a circle with centre O and radius r, let OPAQ be a sector and θ (in degrees) be the angle of the sector. A sector always originates from the center of the circle. Now, we know both our variables, so we simply need to plug them in and simplify. 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? In fact, a quadrant and a semicircle form a sector of the circle. The area of a segment is the area of the corresponding sector minus the area of the corresponding triangle. 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. Step 2: Use the proportional relationship. We know that a full circle is 360 degrees in measurement. 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. Since the cake has volume, you might as well calculate that, too. Thus, when the angle is θ, area of sector, OPAQ = $$\frac{\theta }{360^{o}}\times \pi r^{2}$$. A sector is a section of a circle. The distance along that curved "side" is the arc length. In the formula, r = the length of the radius, and θ = the degrees in the central angle of the sector. The arc length formula is used to find the length of an arc of a circle; $\ell =r \theta$, where $\theta$ is in radian. Now that you know the formulas and what they are used for, let’s work through some example problems! Your email address will not be published. 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