Calculate the area of a circular ring whose outer and inner radii are 12 and 10 cm.

• A. 118.16 cm²
• B. 128.16 cm²
• C. 138.16 cm²
• D. 148.16 cm²

To find the area of a circular ring, you need to calculate the area of the outer circle and subtract the area of the inner circle. The formula for the area of a circle is given by:

Area Formula

Area = π × r²

Step 1: Calculate the Area of the Outer Circle

The outer radius (R) is 12 cm. Thus, the area of the outer circle is:

Area_outer = π × (12)² = π × 144

Area_outer ≈ 452.39 cm² (using π ≈ 3.14)

Step 2: Calculate the Area of the Inner Circle

The inner radius (r) is 10 cm. Therefore, the area of the inner circle is:

Area_inner = π × (10)² = π × 100

Area_inner ≈ 314.16 cm²

Step 3: Find the Area of the Circular Ring

Now, subtract the area of the inner circle from the area of the outer circle:

Area_ring = Area_outer - Area_inner

Area_ring ≈ 452.39 cm² - 314.16 cm² ≈ 138.23 cm²

Final Answer

The area of the circular ring is approximately 138.16 cm². Therefore, the correct option is:

• C. 138.16 cm²