To find the area of the circular box cover, we need to subtract the area of the hole from the total area of the cover.
The area of the cover can be calculated using the formula for the area of a circle:
Area = π * radius²
First, we need to convert the diameter of the cover and the diameter of the hole to their respective radii:
Radius of the cover = Diameter / 2 = 10.16 cm / 2 = 5.08 cm
Radius of the hole = Diameter / 2 = 20.42 mm / 2 = 10.21 mm (convert to centimeters: 10.21 mm = 1.021 cm)
Now, we can calculate the areas:
Area of the cover = π * (Radius of the cover)² = π * (5.08 cm)² ≈ 80.860 cm²
Area of the hole = π * (Radius of the hole)² = π * (1.021 cm)² ≈ 3.277 cm²
Finally, subtract the area of the hole from the area of the cover to get the area of the circular box cover:
Area = Area of the cover - Area of the hole ≈ 80.860 cm² - 3.277 cm² ≈ 77.583 cm²
Therefore, the area of the cover is approximately 77.583 square centimeters (rounded to three decimal places).