Final answer:
The time required to polish the entire surface of a telescope lens can be found using a ratio of the area already polished and the time taken for it. The technician can polish at a rate of 3 mm²/s, and therefore, it will take 2107 seconds to polish the entire area of 6322 mm².
Step-by-step explanation:
The question is asking how long it will take a technician to polish the entire surface of a telescope lens, given the area of the lens and the time it takes to polish a smaller, specified area. To calculate the time required, we apply the concept of ratios.
First, we find out how much area the technician can polish in one second by dividing 135 mm2 by 45 s, which gives us the polishing rate per second. Next, we divide the total area of the lens, 6322 mm2, by the rate per second to find out how many seconds it will take to polish the entire lens. This is a straightforward proportion problem commonly studied in middle school math.
Using this method, the calculation would be as follows:
Rate = 135 mm2 / 45 s = 3 mm2/s
Total time = 6322 mm2 / (3 mm2/s) = 2107 s (which can be converted into minutes by dividing by 60).