Final answer:
To find the surface area of the circular part with a hole, calculate the area of the large circle and subtract the area of the smaller hole. The final surface area rounded to the nearest square millimeter is 92,500 mm².
Step-by-step explanation:
To find the surface area of the circular part of an object, we first calculate the area of the large circle using its radius, and then subtract the area of the hole in the center, which also forms a smaller circle.
The diameter of the large circle is given as 198 mm. Therefore, its radius is half of that, which is 99 mm or 0.099 m. The formula to calculate the area of a circle is A = πr².
For the large circle: A = π(0.099 m)² = 0.030801 π m². When we use π as approximately 3.1415927, the area becomes A ≈ 0.030801 × 3.1415927 m², which is about 0.0968 m² when rounded to four significant figures.
Next, we need to find the area of the hole. Its diameter is 42 mm or 0.042 m, so the radius is 0.021 m. Using the same area formula for the small circle: A = π(0.021 m)² = 0.001381 π m², which is approximately 0.0043 m².
To find the surface area of the circular part with the hole, we subtract the area of the small circle from the area of the large circle: 0.0968 m² - 0.0043 m² = 0.0925 m², which, when rounded to the nearest square millimeter, is 92,500 mm².