You will also want to know that the number of radians of arc in a circle is 2π Circumference Then you need to multiply that by pi and the diameter of the circle. When measuring the circumference of the arc of a circle, you will need to take the arc degree and divide it by 360 (the total number of degrees in a circle). If you’re asked to find the area of a circle, use this formula: While these key formulas will be provided for you, I recommend that you memorize them so that you don’t have to waste your limited time flipping to the reference section during the test. Now that you know key terms as well as the different ways to measure a circle, you will be able to understand the important circle formulas that you’ll need to know for the SAT and ACT. Remember that a complete circle is always 360 degrees, and you will be able to measure the arcs with ease. Likewise, if you were trying to measure the angle of the arc for a quarter of the circle, you would take 360 degrees and divide it by 4 to get 90 degrees. To measure a part of a circle, you will need to see how that part fits within the allotted 360 degrees.įor instance, if you were trying to measure the angle of the arc for one half of the circle, you would take 360 degrees and divide it by half to get 180 degrees. On standardized tests, you will largely rely on degrees instead.Ī circle is 360 degrees. While you will need to learn about radians for geometry and other math classes, you will not typically use this measurement very often on the SAT or the ACT. When an arc of a circle has the same length as the radius of that same circle, the angle of that arc is equivalent to one radian. Measuring a circleĬircles can be measured using two different units: radians and degrees.Ī radian is a unit that determines the measurement of an angle. Once you are familiar with these terms, you will be able to use various formulas to solve circle questions on the SAT and ACT Math sections. Pi (π): Pi, which is approximately equivalent to 3.1415926 is the ratio of the circumference of a circle to its diameter.Radius (r): The length of a line segment that connects the center of the circle with a set point on a circle (half of the diameter).Diameter (d): The length of a line segment that marks the largest distance between two points on a circle.Arc: A curved portion of a circle that lies between two set points.Circumference (c): The distance around the circle. There are a few terms you will need to know about circles before you start measuring them or using any other circle formulas: This set of points forms the closed, round, two dimensional-shape that we call a circle. While it might seem self-explanatory, it is critical that you know exactly what a circle is before you take the SAT or ACT.Ī circle refers to specific points on a plane that are also equidistant from a single point, known as the center of the circle. This guide will give you all the information you need to know about circles so that you can answer each and every circle-related question you face on test day. As such, you should be familiar with how to calculate the area, circumference, radius, diameter, degrees, arcs, and points of a circle. When you’re aiming for the 99th percentile, every question counts. While questions on circles will not make up the majority of your SAT or ACT Math questions, you should expect to see a small handful of them on the test. If you are aiming for a perfect score on the math sections of the SAT or ACT, you are going to need to know a thing or two about circles.
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