Circles room a common shape. You view them all over—wheels ~ above a car, Frisbees passing with the air, compact discs carrying data. These are all circles.
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A circle is a twodimensional figure similar to polygons and quadrilaterals. However, circles space measured differently than these other shapes—you even have to usage some different terms to describe them. Let’s take it a look at this interesting shape.
A circle represents a set of points, every one of which space the exact same distance away from a fixed, center point. This fixed suggest is dubbed the center. The distance from the center of the circle to any allude on the circle is dubbed the radius.
When 2 radii (the many of radius) are put together to form a line segment across the circle, you have a diameter. The diameter the a one passes with the center of the circle and also has that endpoints on the one itself.
The diameter of any circle is 2 times the length of the circle’s radius. It have the right to be represented by the expression 2r, or “two time the radius.” for this reason if you understand a circle’s radius, you deserve to multiply that by 2 to discover the diameter; this also way that if you know a circle’s diameter, you can divide by 2 to find the radius.
Example  
Problem  Find the diameter the the circle.


 d = 2r d = 2(7) d = 14  The diameter is two times the radius, or 2r. The radius that this one is 7 inches, therefore the diameter is 2(7) = 14 inches. 
Answer  The diameter is 14 inches. 
Example  
Problem  Find the radius the the circle.


 The radius is fifty percent the diameter, or . The diameter that this circle is 36 feet, so the radius is feet.  
Answer  The radius is 18 feet. 
Circumference
The distance around a one is dubbed the The distance about a circle, calculation by the formula C =
")">circumference. (Recall, the distance about a polygon is the perimeter.)
One interesting property about circles is the the ratio of a circle’s circumference and also its diameter is the same for all circles. No matter the dimension of the circle, the ratio of the circumference and diameter will certainly be the same.
Some actual dimensions of various items are noted below. The measurements are exact to the nearest millimeter or quarter inch (depending top top the unit of measure up used). Look at the ratio of the circumference to the diameter because that each one—although the items room different, the proportion for every is around the same.
Item  Circumference (C) (rounded come nearest hundredth)  Diameter (d)  Ratio 
Cup  253 mm  79 mm  
Quarter  84 mm  27 mm  
Bowl  37.25 in  11.75 in  
The circumference and also the diameter space approximate measurements, due to the fact that there is no precise method to measure up these dimensions exactly. If you were able to measure up them much more precisely, however, girlfriend would uncover that the proportion would move towards 3.14 for each that the items given. The mathematical surname for the ratio is The proportion of a circle’s circumference come its diameter. Pi is denoted through the Greek letter
")">pi, and also is stood for by the Greek letter .
is a nonterminating, nonrepeating decimal, so the is impossible to write it the end completely. The first 10 number of are 3.141592653; it is frequently rounded to 3.14 or approximated as the portion . Keep in mind that both 3.14 and also are approximations of, and also are provided in calculations whereby it is not necessary to be precise.
Since you understand that the ratio of circumference to diameter (or ) is constant for all circles, you have the right to use this number to uncover the one of a one if you know its diameter.
= , for this reason C = d
Also, since d = 2r, climate C = d = (2r) = 2r.
Circumference of a Circle To uncover the circumference (C) of a circle, use one of the complying with formulas: If you recognize the diameter (d) the a circle: If you understand the radius (r) the a circle: 
Example  
Problem  Find the circumference of the circle.
 
 To calculate the circumference offered a diameter the 9 inches, use the formula . Usage 3.14 as an approximation for . Since you space using one approximation for , you can not give specific measurement of the circumference. Instead, you use the price to indicate “approximately equal to.”  
Answer  The circumference is 9 or approximately 28.26 inches. 
Example  
Problem  Find the circumference of a circle v a radius of 2.5 yards.  
 To calculate the circumference of a circle given a radius of 2.5 yards, usage the formula . Usage 3.14 as an approximation for.  
Answer  The one is 5 or about 15.7 yards. 
A circle has a radius that 8 inches. What is that circumference, rounded to the nearest inch? A) 25 inches B) 50 inches C) 64 inches2 D) 201 inches Show/Hide Answer A) 25 inches Incorrect. You multiplied the radius time ; the correct formula because that circumference as soon as the radius is given is The correct answer is 50 inches. B) 50 inches Correct. If the radius is 8 inches, the exactly formula because that circumference once the radius is provided is The correct answer is 50 inches. C) 64 inches2 Incorrect. Girlfriend squared 8 inch to come at the price 64 inches2; this will provide you the area that a square with sides the 8 inches. Remember that the formula because that circumference when the radius is offered is . The exactly answer is 50 inches. D) 201 inches Incorrect. That looks choose you squared 8 and also then multiplied 64 through to come at this answer. Remember the the formula for circumference once the radius is offered is . The correct answer is 50 inches. Area is critical number in geometry. You have already used the to calculate the one of a circle. You use when you are figuring the end the area that a circle, too.
