What is the Circumference of a Circle The distance around a closed curve is called as the circumference of the circle. It is also defined as the length around the circle. The circumference of a circle is measured in linear units like inches or centimeters. Circumference of a Circle Formula The formula of circumference of a circle is given by the following formula, Circumference, C = 2 * π * r where, r is the radius of the circle. and pi is a constant value and is equal to 3.14 The circumference of a circle can be calculated by its diameter using the following formula: Circumference, C = π * D Where, value of π is a constant and its value is approximately 3.14159265358979323846.... or 22/7 to be more precise and D is the diameter of the circle. To simplify calculations the value of π is rounded to 3.14. The diameter of a circle is twice its radius. Therefore, Circumference, C = 2 π r Circumference of a Circle Examples
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Below are the examples on circumference of a circle Example 1: Find the circumference of a circle given that its radius is 10. Solution: The circumference is always multiply by 2 the length of the radius, Formula Circumference of circle = 2 r Circumference = 2 x 10 x = 62.8 Example 2: Find the circumference of a circle known that area of the circle is 153.86 Solution: Step 1: Find the radius of the circle . r2 = 153.86 r2 = r2 = 49 Learn More Radius of a Circle
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r=7 Step 2: Then calculate the Circumference of circle, Circumference of circle = 2 r =2*7* = 43.96 Therefore, the circumference of the circle is 14. Example 3: Find the circumference of a circle known that its radius is 16 Solution: The circumference is always multiply by 2 the length of the radius, Circumference of circle = 2 r Circumference = 2 x 16 x = 100.48
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What is the Pythagorean Theorem The Pythagorean theorem is related to the study of sides of a right angled triangle. It is also called as pythagoras theorem. The pythagorean theorem states that, In a right triangle, (length of the hypotenuse)2 = {(1st side)2 + (2nd side)2}. In a right angled triangle, there are three sides: hypotenuse, perpendicular and base. The base and the perpendicular make an angle of 90 degree with eachother. So, according to pythagorean theorem: (Hypotenuse)2 = (Perpendicular)2 + (Base)2 In the above figure1, c2 = a2 + b2 Therefore, Hypotenuse (c) = √ (a2 + b2) From the above figure 2, Δ ABC is a right angled triangle at angle C. From C put a perpendicular to AB at H.
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Now consider the two triangles Δ ABC and Δ ACH, these two triangles are similar to each other because of AA similarity. This is because both the triangle have a right angle and one common angle at A. So by these similarity, ac = ea and bc = db a2 = c*e and b2 = c*d Sum the a2 and b2, we get a2 + b2 = c*e + c*d a2 + b2 = c(e + d) a2 + b2 = c2 (since e + d = c) Hence Proved. Euclid Proof of Pythagorean Theorem According to Euclid, if the triangle had a right angle (90 degree), the area of the square formed with hypotenuse as the side will be equal to the sum of the area of the squares formed with the other two sides as the side of the squares. From the above figure 3, the sum of the area covered by the two small squares is equal to the area of the third square. Here, a2 is the area of the square ABDE, b2 is the area of the square BCFG and c2 is the area of the square ACHI.
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