Area and circumference of a circle Grade 9 ★ Knowledge
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Exercise books for all videos: http://shop.strandmathe.de/ Facebook: / strandmathe Instagram: / strandmathe Twitter: / strandmathe The circumference and area of a circle are calculated using the following formulas: U = 2 ∙ π ∙ r and A = π ∙ r² The placeholder π stands for the circle number. It is an irrational number that is approximated with π = 3.14159…. The circumference and area can therefore be calculated as a function of the radius r. The approximation of the circle number comes from breaking down a circle into an infinite number of identical isosceles triangles. Their bases can be determined and added together to give the circumference, or their areas can be added together to give the area. Sophie: “It’s 1.2 kilometers from the hotel to the beach. I always cycle this route." Jonas: "Have you ever thought about how many revolutions the wheel makes on the way?" To find an answer to this question, we first need to know the size of a tire. Sophie's mountain bike has 26-inch wheels. This corresponds to a diameter of approximately 65 cm or a radius of 65 cm∶2 = 32.5 cm. With this information and the formula for calculating the circumference of a circle, you can now continue working. The tire or bicycle travels exactly the length of the circumference in one revolution. So you first calculate the circumference, then divide the distance by the circumference to get the number of revolutions. The mathematical equations are: U = 2 ∙ π ∙ r = 2 ∙ π ∙ 32.5 cm = 204.2 cm = 2.042m Revolutions = distance/circumference = 1200 m / 2.042 m ≈ 587.7 Jonas: “So a wheel makes 587.7 revolutions. Of course, you can also do the calculation the other way round and determine how far you can go with 800 revolutions, for example.”
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