The area of an annulus refers to the section enclosed by two concentric circles. When calculating the area of an annulus, our approach is to decompose it into two circles and then calculate the difference in their areas. Specifically, we first calculate the area of the outer circle, which is π multiplied by the square of the outer radius (πR^2).
Then we calculate the area of the inner circle, which is π multiplied by the square of the inner radius (πr^2). Finally, by subtracting the area of the inner circle from the area of the outer circle, we obtain the area of the annulus, which is π multiplied by the difference between the square of the outer radius and the square of the inner radius, expressed as π(R^2-r^2).
The formula for the area of an annulus is: S = π(R^2 – r^2) or S = π(RR – rr), where R represents the radius of the outer circle and r represents the radius of the inner circle.
The derivation of the annulus area formula can be achieved by decomposing the annulus into two circles and then calculating the difference in their areas. In practical applications, the annulus area formula can be used to calculate the areas of objects such as tires, pipelines, circular flowerbeds, and so on.
The annulus area formula has extensive applications in daily life. For instance, we can use it to calculate the area of a tire, which helps us determine its size and applicable range. Similarly, we can utilize the formula to calculate the area of a pipeline, enabling us to assess its flow rate and transport capacity. Furthermore, the formula can also be applied to calculate the area of a circular flowerbed, assisting us in determining its size and the number of plants it can accommodate.
For example:
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If a pipeline has an outer circle radius of 20 centimeters and an inner circle radius of 15 centimeters, its area can be calculated using the annulus area formula: π((20^2)-(15^2))=π(400-225)=π(175)≈549.78 square centimeters. This result can help us determine the flow rate and transport capacity of this pipeline.
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For a circular flowerbed with an outer circle radius of 1 meter and an inner circle radius of 0.8 meters, its area can be calculated using the annulus area formula: π((1^2)-(0.8^2))=π(1-0.64)=π(0.36)≈1.13 square meters. This result can assist us in determining the size of the flowerbed and the number of plants that can be planted.
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For an annular swimming pool with an outer circle radius of 5 meters and an inner circle radius of 3 meters, its area can be calculated using the annulus area formula: π((5^2)-(3^2))=π(25-9)=π(16)≈50.27 square meters. This result can help us assess the size and water capacity of the swimming pool.
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Calculating the area of the Olympic rings flag. The flag consists of five concentric circles, with each circle having a specific radius: the outer circle radius R=1, and the inner circle radius r=0.7. Using the annulus area formula, the area of the flag can be calculated as: π((1^2)-(0.7^2))=π(1-0.49)=π(0.51)≈1.61 square centimeters. This result provides us with an understanding of the size and area of the Olympic rings flag.
Related articles: “Formula for the Area of a Circle,” “Formula for the Area of an Ellipse,” “Formula for the Surface Area of a Sphere,” “Formula for the Area of an Annulus,” “Formula for the Surface Area of a Cylinder,” “Formula for the Lateral Area of a Cylinder,” “Formula for the Surface Area of a Cone,” “Formula for the Lateral Area of a Cone.”
