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\n<\/p><\/div>"}, Practice Problems to Calculate Radius of a Circle. The easiest way to find the radius is by dividing the diameter in half. Area of a Sector Calculator So converting = 117 to radians and using r = 3.5 in Equation 4.3.1 for the area A of the sector, we get = 117 = 180 117 = 2.042 rad A = 1 2 r2 = 1 2 (3.5)2 (2.042) = 12.51 m2 . You cut it into16even slices; ignoring the volume of the cakefor now, how many square inches of the top of the cake does each person get? A sector extends from the center, or origin, of the circle to its circumference and encompasses the area of any given angle that also originates from the center of the circle. Were committed to providing the world with free how-to resources, and even $1 helps us in our mission. It only takes a minute to sign up. Step 2: Divide each side by $0.471$ rounded to nearest hundredth. Why Extend Volume is Grayed Out in Server 2016? Try this Drag one of the orange dots that define the endpoints of the sector. Using \(s=6 \) and \(r=9 \) in Equation \ref{eqn:sectorarc} for the area \(A \), we get, \[ A ~=~ \tfrac{1}{2}\,rs ~=~ ~=~ \tfrac{1}{2}\,(9)\,(6) ~=~ \boxed{27~\text{cm}^2} ~. However, it is possible, by construction, to locate the center of such a circle, and then, simply by physically measuring, determine the radius. Sectors, Areas, and Arcs | Purplemath PDF Radians, Arc Length, and Area of a Sector - UH ", all of it with my teacher, so I favorited the page to come back again when I get there! This was quite comprehensive, and attractively narrated on various methods of measuring D, r,, C etc. The answer is r=12. Using the formula $$L=2\pi r\times\frac{\theta}{360}$$ where $L$ is arc length, you can rearrange to give: Sector Calculator - TrigCalc.com If you dont know the diameter but you know other measurements, such as the circles circumference (C=2r{\displaystyle C=2\pi r}) or area (A=r2{\displaystyle A=\pi r^{2}}), you can still find the radius by using the formulas and isolating the r{\displaystyle r} variable. . Once I've got that, I can plug-n-chug to find the . Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Be careful, though; you may be able to find the radius if you have either the diameter or the circumference. When the central angle formed by the two radii is90, the sector is called aquadrant(because the total circle comprises four quadrants, or fourths). 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. 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 in31and 9 inches: If, instead of a central angle in degrees, you are given theradians, you use an even easier formula. The best answers are voted up and rise to the top, Not the answer you're looking for? Finding the radius of a circle when given the area of the sector and the measure of the central angle 5 Ways to Calculate the Area of a Circle - wikiHow 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. The formula for calculating the area of a sector: Area of a sector = (/360) [r] Where; A = Area of the Sector r = Radius of the Sector Unlike triangles, the boundaries of sectors arenotestablished by line segments. Learn more about Stack Overflow the company, and our products. Exampler=6.69=2.59{\displaystyle r={\sqrt {6.69}}=2.59}. (\text{Area of sector \(GBF\)}) \right)\\ \nonumber Enjoy! \end{alignat*} \nonumber \], \[\nonumber \begin{align*} Math Calculators Geometry Calculators Arc Length Calculator Find the arc length of a sector by entering the central angle and radius in the calculator below. (1.696 - \sin\;1.696) ~=~ \boxed{1.408} Divide the length of the arc by the length of the circumference. \nonumber \]. . $31.85=r$. Area of a Circle Calculator Given the diameter,d, of a circle, the radius,r, is: Given the circumference,Cof a circle, the radius,r, is: Once you know the radius, you have the lengths of two of the parts of the sector. What's the significance of a C function declaration in parentheses apparently forever calling itself? How do I find the radius of a circle when I know the arc length and the central angle? Sector area. ExampleIf using 3.14 for {\displaystyle \pi }, you would calculate:r=213.14{\displaystyle r={\sqrt {\frac {21}{3.14}}}}r=6.69{\displaystyle r={\sqrt {6.69}}}If your calculator allows you to enter the whole formula on one line, that will give you a more accurate answer. Find the Area of the Shaded Region of a Circle: Clear Examples First, write the formula. Key Skill - Find the radius of a sector given its area and angle. Were committed to providing the world with free how-to resources, and even $1 helps us in our mission. X Next, begin isolating the r by dividing both sides of the equation by 3.14. wikiHow's Content Management Team carefully monitors the work from our editorial staff to ensure that each article is backed by trusted research and meets our high quality standards.

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