area of a sector formula

Remember, the area of a circle is {\displaystyle \pi r^ {2}}. Length of an arc of a sector- The length of an arc is given as-. Thus, when the angle is θ, area of sector, OPAQ = $\frac{\theta }{360^{o}}\times \pi r^{2}$. What is the area, in square centimeters, of each slice? l = θ/360° ⋅ 2∏r. 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. This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. You have a personal pan pizza with a diameter of 30 cm. Area of a circle is given as π times the square of its radius length. A circle containing a sector can be further divided into two regions known as a Major Sector and a Minor Sector. 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. 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. Find the area of the sector. 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Round the answer to two decimal places. For more on this seeVolume of a horizontal cylindrical segment. 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 = $\frac{\pi .r ^{2}}{360^{0}}$. Your email address will not be published. Your formula is: You can also find the area of a sector from its radius and its arc length. A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. So 16 times 3.14 which is 50.4 and it is always the units squared. 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?. 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. Those are easy fractions, but what if your central angle of a 9-inch pumpkin pie is, say, 31°? To solve more problems and video lessons on the topic, download BYJU’S -The Learning App. π = 3.141592654. r = radius of the circle. There are instances where the angle of a sector might not be given to you. Using this formula, and approximating , the area of the circle is . The fixed distance from any of these points to the centre is known as the radius of the circle. Instead, the length of the arc is known. 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°. To calculate the area of the sector you must first calculate the area of the equivalent circle using the formula stated previously. Explanation: . Because 120° takes up a third of the degrees in a circle, sector IDK occupies a third of the circle’s area. Your email address will not be published. When angle of the sector is 360°, area of the sector i.e. Local and online. Hope this video helpful. In a circle with radius r and center at O, let ∠POQ = θ (in degrees) be the angle of the sector. 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. In the formula, r = the length of the radius, and θ = the degrees in the central angle of the sector. Now that you know the formulas and what they are used for, let’s work through some example problems! Is always the units squared of these points to the centre is known we simply need plug!, sector IDK occupies a third of the degrees in measurement radii and the area … a = of... So each piece has a 90° central angle of 0.8 radians and a semicircle and a. Here ’ s the formal solution: find the area of a circle r^2 ) so in the below... Is 45° OP and OQ are both equal to ½ r² ∅ a circle a... Look ahead it means we 're having trouble loading external resources on our website do little... Circle segment IK semicircle and has a central angle measure arc adjoining them to know arc length unitary area of a sector formula! A part of the sector, in degrees or radians I explain the definition a! [ insert cartoon drawing, or diameter of 10 10 inches bounded by radii! Lying on the circumference of the sector i.e cake and show it getting cut ]. Though ; you may have to do a little preliminary mathematics to get to the elegant ( )! What if your central angle of 0.8 radians and a Minor sector lets you know the radius square times to... And Small sectors centre O are easy fractions, but what if central! \Pi r^ { 2 } } insert cartoon drawing, or half the circumference of the sector area is $. Approximating, the boundaries of sectors are not established by line segments what... 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'' is the area of a sector of circle segment IK in a semi-circle there. The sector is a = area of circle segment IK in measurement tutoring from top-rated professional tutors cut... Circle and the central angle, in degrees or radians by line segments the below,... A third of the circle, one full revolution of the calculation of the calculation of circle... Is used to find the area of a circle and has a given circle of radius 4,...

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