Calculating the area of a circular ring may seem like a daunting task, but with the right formula and knowledge, it can be a straightforward process. In this comprehensive guide, we will take you through step-by-step instructions on how to calculate the area of a circular ring. Let’s get started!

What is a Circular Ring?

A circular ring, also known as an annulus, is a region bounded by two concentric circles. It resembles a donut, with a hollowed-out center. To calculate its area, we need to know the outer and inner radii of the ring.

Step 1: Measure the Outer and Inner Radii

The first step is to measure the outer and inner radii of the circular ring. The outer radius (R) is the distance from the center of the ring to the outer circle, while the inner radius (r) is the distance from the center to the inner circle.

Step 2: Calculate the Area of the Outer Circle

To find the area of the outer circle, we need to use the formula for the area of a circle: A = π * R^2. Simply square the value of the outer radius and multiply it by π (pi). The result will give you the area of the outer circle.

Step 3: Calculate the Area of the Inner Circle

Next, we calculate the area of the inner circle using the same formula: A = π * r^2. Square the value of the inner radius and multiply it by π to obtain the area of the inner circle.

Step 4: Subtract the Inner Circle Area from the Outer Circle Area

Now that we have the areas of both the outer and inner circles, we can find the area of the circular ring by subtracting the area of the inner circle from the area of the outer circle. The formula for this is: Area of Ring = Area of Outer Circle – Area of Inner Circle

Step 5: Calculate the Final Area

Apply the formula mentioned in step 4 to find the area of the circular ring. Subtract Area of Inner Circle from Area of Outer Circle. The resulting value will be the area of the circular ring.

Example Calculation

Let’s go through an example to help you understand the process better:

  • Outer Radius (R) = 10 cm
  • Inner Radius (r) = 5 cm

Using the formula for the area of a circle, we find:

  • Area of Outer Circle = π * (10^2) = 100π cm^2
  • Area of Inner Circle = π * (5^2) = 25π cm^2

Subtracting the area of the inner circle from the area of the outer circle:

  • Area of Ring = 100π – 25π = 75π cm^2

So, for this example, the area of the circular ring is 75π cm^2.

Calculating the area of a circular ring is simple if you follow these steps. Remember to measure the outer and inner radii accurately and apply the formulas correctly. Using the example provided, you can try different values to practice and gain a deeper understanding of how to calculate the area of a circular ring. Happy calculating!

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